Your nara is not going to take the whole day if you just want to see deer and todaiji. The deer are like right smack outside todaiji's entrance. You could like add plan to see some mausoleum (this will require some bus rides, so research a bit) or you can opt to go 1/2 day Nara (you can throw in kasuga taisha after visiting todaiji its walkable distance also the road leading up to kasuga also bazillion deers.....) Then go to kyoto and enjoy gion during the evening (its more instagrammable at dusk and night...) Kyoto, if you just want to do the usual tourist spot of kiyomizudera and its downtown dont need a whole day. But best give kyoto at least a daytrip and plan a route)

You could spend whole day in Nara, it reallt depends on how many mausoleums and temple/shrines you wanna see there. Ah don't forget that shopping street with the viral mochi pounding man 👍

Fushimi inari taisha is best you go early morning. Less people... But since no chinese tourist should be ok 😂😂😂 arashiyama is a very small bamboo forest... The picture makes it look like as if its super big but after go there.... expectation 100% reality 30% lol but if you go during scenic times (spring or autumn) take the scenic train ride before going to the bamboo forest

P/S dotonbori and shinsaibashi literally at same spot

P/S2: you could also go further down from fushimi inari like early morning go fushimi inari, after climbing up and down those torii, have lunch then take the train to Fushimi for a quick stop to a sake museum (it even has sake tasting and you can also obviously buy sake. Precovid every entry ticket gets you a bottle of sake, idk if they still do that. The museum is called Gekkeikan) and after sake museum, depending how much time you dwaddle therw, you can take the train ride to the motherload town of uji matcha, Uji. Then head back to kyoto or osaka depending where you are based

Unless you made another post before that post i replied to, i must've missed when you mention you plan to go. Please replied to me again so i can see a notification. I will give a better guide and explanation to you this evening after i finished work. Is that alright?  If you got a lot of luggage suggest you stay namba area. Thats where the airport transfer is. Namba also super convenient. Also another thing, if you plan to bring a 5 yo kid to fushimi inari taisha, i hope your kid is a really good no tantrum kid or you and wifey got a lot of stamina cause you gonna be needing it hauling your kid up a lot of steps. The torii is an ascent. Also some steps are narrow and mossy, blah2. If you have ambition to go all the way to the top, have a contigency plan 😅 if not gonna have very unhappy kid and parents

Edit: woops sorry i see you asking for december... A pity you wil miss the koyo alrd... If you go now is best time. Will be beautiful. I can rework your itinerary a bit and give some suggestions. You can consider Kobe also.just barely half an hour on a normal train. You can just buy the normal ticket. Can take ropeway up nunobiki garden and have a nice cooling time and cool view of kobe city then walk back down the ropeway first station then have a nice walk pushing stroller around all the special western district and kobe chinatown 👍 then can enjoy kobe beef too

take the airport express train from KIX that ends at Namba, closest you can get to Shinsaibashi afaik. otherwise its a transit of trains within the Osaka Metro/Subway line (Midosuji i think). bad news is airport express can get crowded as many uses it to fast transit to city

as for cold, japan cities down south in winter shouldnt be as terrible as hokkaido. i was in Osaka/Kyoto in Jan, coldest was 0C and avg 2-4C daily. if sun out longer, then itll be 6C max. just pray no strong winds, that one i suggest a hardshell windbreaker to pair with your warm clothing

Okay, so here are some of my tips and info for Osaka. Hope it can be useful for you.

IF you're doing:

ROUND TRIP OSAKA. ONLY PLAN TO SIGHTSEE AROUND OSAKA CITY, KYOTO, AND/OR KOBE. Then,

a. you don’t need a JR PASS of any sort.
b. You do however can make use of various other passes like;
a. Osaka city 1D metro pass to go around Osaka City
b. You can take advantage of Osaka Amazing Pass
                    i. Offered as a 1D or 2D pass
                    ii. (it is bundled with all day metro and bus pass and works on Nankai, Hankyu, Hanshin, Keihan, Kintetsu trains)
                    iii. Offered you to enter some sight-seeing spots around the city for free instead of having to pay Admission.

c. In Kyoto, bus pass is more superior than subway pass. Though do note driving in Kyoto City is a nightmare (even parking is a pain).
        However since you have a stroller, maybe do the Kyoto subway. It’s not as convenient as the bus, but at least you can squeeze in a stroller easier.
d. If you don’t mind the extra bit of spending and lazy to buy the above-mentioned passes, just get yourself an IC card (ICOCA) and use it as a normal MRT card.
        Just top up when needed. Though if you’re a first-timer in Osaka, I do say Amazing Pass is quite a nice deal.
e. There are other passes offered by other rail companies besides JR you can use to go to places like Nara, Uji, Wakayama, Shiga. Examples:
            i. Kintetsu Rail Pass (1D is 1500 yen) Pass is offered as a one day, two days, or five days option. The 1D pass will let you travel from Namba to Nara or Kyoto to Nara sufficiently on the Kintetsu Line.
                It’s also the fastest line for Kyoto-Nara.
            ii. Hanshin also offer a 1D tourist pass to let you ride unlimited rides on their trains. You can make use of it to go to Kobe. The pass is about 500 yen. Or you can also just pay normal fare.
                Hanshin, JR and Hankyu have route from Osaka to Kobe.

f. If you plan to sight-see around Osaka City, you could opt to base yourself at Shinsaibashi or Namba/Nipponbashi area. You can even consider quieter, yet still accessible area like Daikokucho (which is like a 5 mins walk to
        Namba Park, close to Shinsekai. And depends on how much of a walking person are you, you can stroll through Namba to Kuromon Market. All are within walking distance.
g. Namba is also where the Airport transfer is at, so you can save yourself the annoyance of lugging pieces of luggage through Osaka Metro (which is always packed... esp Midosuji line) to reach the airport.
h. Namba area is great as a base for city exploration and also to access other areas like Wakayama. Also, there’s SIX (yup) Namba stations owned by different rail companies... So don’t get confused and get to know who owns
        what.
i. Namba is also convenient to go to USJ, kaiyukan, ferris wheel.
j. December is also a great time for the annual Christmas Lights Illumination at Midosuji.
k. If you’re planning to take a lot of shinkansen rides and no deep dive Osaka City exploration. It’s better to base yourself at the north (kita) area of Osaka like around Umeda or Shin-osaka.
KYOTO

a. You could easily squeeze Kiyomizudera, Gion district, the downtown shopping area incld Nishiki Market for ½ day. Near to Kiyomizudera is Yasaka Shrine (it’s also located in a big ass park,
        if you walk that, you will take up a lot of time). So you could do a route of Kiyomizudera -> then walk through the famous Ninen and Sannen zaka (this will connect you through all the way to Yasaka Shrine).
          Yasaka Shrine sits at a T junction facing Kyoto-Kawaramachi that will connect you to Gion and the downtown area.
b. Kinkakuji and Ginkakuji are both a little out of the way (also opposide direction of each other).
c. Since you’re interested in going to Arashiyama, you should try the Sagano Scenic Railway. Then you can walk through the Bamboo Forest and also consider a boat ride on Hozugawa.
        This whole itinerary would take you just half a day.

NARA

a. Nara itself has a lot to offer, but most people only know deer, todaiji, and maybe kasuga-taisha. But Nara actually also have a “mountain” (tbh it should be a hill) but you might not be able to access it in december.
If you’re like a history afficianado, Nara is also the location for a few mausoleums of past emperor and empress of Japan. The most famous one will be the mausoleum of Emperor Kaika and another is the mausoleum of Empresss Jingu. They are however, a little not that convenient to get to compared to famous spots like Todaiji, kasuga-taisha and kofuji. So, if you only plan to do the general sights, half day trip is more than sufficient.

As mentioned in my first reply, you could after visit to Fushimi Inari, take the train a few stations down to the sake brewery or just go straight to Uji and do a ½ day tour there. You could also do a Shiga/Lake Biwako day trip from Kyoto. There’s Hieizan in Shiga (you can go up with a ropeway) that offer nice view of Japanese primodial forest and also view of Lake Biwako from the observatory on top. Then could go to Lake Biwako and enjoy ferry cruises (they got all sorts! One type was even a kind of American style ferry called Michigan Cruise.
If you want to do a 1 day or 1/2 day itinerary to Kobe, I would suggest first go to Nunobiki Garden (I recommend it all my friends that wanted to go Kobe). You can take the ropeway up there (the ropeway station base is also conveniently located right around the corner at Sannomiya station) The Garden offers a view of Kobe City. There’s also a really nice café and shop at the top of the garden and even has a foot bath.
After you come down from the garden, you can stroll through Kitano-cho (the western district with a lot of interesting period buildings, some of them requires a fee to enter). From Kitano-cho it is an easy walk towards the downtown (to enjoy kobe beef meal) and Kobe Chinatown. Kobe Chinatown is also a really easy walk to nearby Kobe Port (where you can still see some preserved remmants of the great Kobe earthquake in 1995) and Port tower.

Weather wise in December, Kobe, Osaka and Kyoto are similar. As long as wind doesn’t blow, you’re good. Just layer yourself and prepare a warmer jacket for night time.

As for ryokan recommendations, I can’t really suggest any OTL... I’m a single woman and I don’t consider myself heavily tattooed, but tattoo-ed enough on my body so I don’t really bother about going to onsen that kind of thing. Just too bothersome to find one that will accommodate me. More of an outdoor person. If you want to hike around Japan, I got a lot of recommendations lol) But one thing i would say is find somewhere thats very near Kyoto Station (walkable) or least only 1-2 subway (like at karasuma-gojo) or bus ride away. Any further will just be kinda inconvenient.

Sorry, I wrote it on microsoft word, but then after pasting, realised this forum doesn't accept Word's formatting. I hope it's not that confusing. If there's any confusing part, feel free to ask, I'll try to explain better.
Regarding this, 99% you could just do that yes. But for the Sagano Rail, I would suggest you buy online, like maybe through middleman app like Klook or KKDAY, sometimes you won't be able to get Sagano on the same day. So best to book that in advance to get the day and time you wanted.
Driving to Kyoto is really pointless (not only that, the train ride from osaka to kyoto is such a short ride...) because unless you plan to go out of Kyoto (still in Kyoto but out of it) the traffic jam is gonna drive you mad. Also parking is a struggle. You cannot just park anywhere and not all lodging offer parking. So you need to take that into consideration (assuming you plan to rent a car the whole time you're there).

Oh, one thing I do have to remind you is that there's a new post covid rules about luggage on shinkansen (though you probably won't be riding any with your itinerary unless you decides to change it)
On certain shinkansen routes like on Tokyo-Osaka/Osaka-Tokyo (Tokaido Shinkansen), Sanyo route (Osaka-fukuoka/fukuoka-osaka) and a few others i don't remember, if your luggage size exceed 250cm and above, you're not allowed on the train, if it is below 250cm but above 160cm, then you need to make seat reservation (green car). You could also consider luggage forwarding service (for like few thousand yen) if you really have a lot of luggage to your next destination so you can travel the train with ease. Some hotels can hook you up with this kind of service, no harm asking.
Yup. that is a good flow so you're not going all over the place and wasting time travelling.
No hate for Shinsekai, I love going there for the little hidden shops with kickass and cheap kushikatsu, but do take note that Shinsekai is a red-light district. (it is also one of the poorer district, was improving regarding homelessness, but that is still a thing... i have not been to osaka post-covid, but shinsekai took a heavy beating during covid-era. Japan as a whole are safer than a lot of country. You can still stay there, but just take note.

Also, if you're staying at Shinsekai, you could take a metro or just walk (it is very close by) to Tennoji and go to Abeno Harukas (one of the tallest skyscraper in Japan and has a observation deck to offer you a non-impeding view of Osaka City. The observation deck requires admission fee. You could have your xmas eve dinner (but usually you gotta book, walk-in on xmas eve/xmas is really about finding a miracle lol) over at Abeno Harukas (got some fancy places with good atmosphere) as well or you could do it over at the Umeda area (also got a lot of fancy places), have a nice dinner then afterwards, then stroll through the xmas lights illumination on Midosuji.

If you do go Kobe, you could still make it a day trip or overnight. Rent a car there and you can include driving to Akashi-kaikyo bridge to the rest of the itinerary or drive to Rokkosan Mountain Farm to enjoy family oriented activities there.

Tbh,if you have more days to spend, i would've suggest you get like JR Kansai Wide pass and go to Tottori (December in Tottori is the season of Matsuba crab and zuwaigani aka snow crab. It's absolutely insanely fresh and cheap when in season, you could rent a car there and also drive all the way to sakaiminato as well, its a port and with a lot of fresh seafood) and further to Hiroshima/Miyajima.
Go where you haven't go in Osaka city area  Also, since Airport Transfer is located at Namba, you could either drop your luggage at the locker there or search for a luggage keeping service. They charge by pieces usually. Just google Luggage storing service namba osaka. it will bring you a list. Make sure it's near the train station though.

Yup, that's the one. 'Sagano Scenic Railway'. Just buy from Klook or KKday and book a day.
Yes. That's right, Osaka itself to Kyoto on normal train is not that long a ride, just about 30 mins.(and by Osaka, I'm saying like from Umeda station/Osaka to Kyoto Station (which is located in the North(kita) side of Osaka). If you're travelling from Shinsaibashi which is the Minami (south) area, it's going to take more than 30 mins. you can check this link for reference about travelling time for the various train lines from Osaka to Kyoto if you feel confused.
Yes, but its gonna be hectic depending on what time you're using it. But if you don't have many pieces it will be okay.

嵯峨野トロッコ列車 冬景色 try this search term and decides for yourself
First and last carriages are stroller friendly and have dedicated stroller space. Other than that, you prolly have to fold up? I'm a single woman, really am not the best person to ask about this. (I'm trying to think hard about my time on the trains if i seen a stroller or not lmao) Maybe try googling OTL
If you're always together with family, maybe mifi? I'm usually a solo traveler and also gotten lazy buying japanese sim...I think i only bought jp sims twice. After that, each time i just buy roaming addon.
I'm on Digi, 14 days jp roaming just cost me 75 rm. not unlimited internet but was enough for what i need (basically google maps, navitime, tabelog). Besides, it comes with call minutes which those jp travel sim doesn't offer. Every telco also has something similar i reckon? I think maxis offers only 1  type of roaming for japan and it's around 99 myr and last 30 days. (digi 30 days jp roaming is 95-30gb internet but weirdly only 30 mins call time)

90% shop will be closing, those open will be chain store restaurant. Theme park will be full of people. Onsen will be ridiculous expensive. Basically either you go hiking or sleep in hotel room or shopping in mall.

Not really. Mostly will be rest & sleep in home. Japan are high stress society. Alot Japananese work until 12am and wake up as early as 5am.
You can go Japan train Station on 5am morning, you will see the crowd already, even 12am midnight, station still got full of people taking last train back home.

I remember watching youtube video, saying the airlines will have some statistics, to determine how many tickets they sell, etc. Based on past experience.

But i think early check in does help with it.

But based on what i saw yesterday... AAX flight was relatively empty. Quiet zone about 30% to 40%. But the "normal" zone still quite full maybe 70% 80%, obviously this number is gut feel, didnt really count. One quick glance, dont see that many rows 3 ppl fully seated.

For fun sharing, although not a good news. Got a friend flying tmr by airasia. Departure time got delayed from 2pm+ to 6pm+. Hopefully dont delay further.

Travelling post covid (especially AA?) is really full of surprises.

you booked sagano romantic train online thru klook or other travel agency?  If you booked thru online, normally redeem ticket location are at Kyoto Station designated spot.

You cannot get Sagano romantic train ticket at Kyoto Station. You can ride Sagano Scenic train from Kameoka or Saga Arashiyama Station. I personally like to take the train from Saga Arashiyama Station towards Kameoka Station. From Kameoka take Hozugawa River Boat Ride back to Arashiyama

NOTE:

IF you take the train from Kyoto Station direct to Kameoka Station, on some route the train line are aligh with Scenic train line, basically already potong stim 
So from Kameoka to Arashiyama scenic wont be any more surprise to you. Everything already potong stim

Sagano Scenic train are based on 1st come 1st serve basic and ticket only available at Kameoka Station / Saga Arashiyama Station only.
Klook are expensive but you got secure ticket.

About the boat, during winter, the boat will be heated up. very comfortable, but the price are on higher side. (4100 Yen per pax)
Once a life time, it was worth. Unless you wanted become like me which go Kyoto more than 100 times, then no need. 

NOTE:

IF you take the train from Kyoto Station direct to Kameoka Station, on some route the train line are aligh with Scenic train line, basically already potong stim 
So from Kameoka to Arashiyama scenic won't be any more surprise to you. Everything already potong stim.

From Kyoto Station don't take JR Train direct to Arashiyama. If you got alot time to spare, Follow my route.
From Kyoto Station > Karasuma Oike Station via Karasuma Subway Line.
Karasuma Oike Station > Uzumasa Tenjingawa Station via Tozai Subway Line.
Uzumasa Tenjingawa Station > Randen-Saga Station via Randen Arashiyama Line (Very classic tram)
Randen-Saga Station walk to Saga-Arashiyama Station

Doesnt matter if the ride is hourly. Its a small train. It cant carry much per ride. If you dont buy DAYS in advance, chances are you won't be able to get in on the day and the time you want. (Or even next train) Last time they used to allow you to stand in the train (which is really lame, you definitely want to sit) but now i think no more.

The boat ticket are sold on the spot at the pier

if both forest and streets try put around 2hrs at least

or even the monkey park also can include

thanks bro! looks like i'll need to hit the brakes on the Osaka 2 day pass, i might just get 1 day since i want to cover these places:
Osaka Castle
Suijyo Bus (Aqualiner)
Umeda Sky Building
Hep Five Ferris Wheel
the next day i plan to take half day to Nara

for the Sagano train, can you buy return ticket at Saga/Arashiyama station?

for the west side of Kyoto, did you start from Fushimi Inari Taisha (south-west) or Higashiyama Jisho-ji (north west)?