ur budget including travel and stay? i didn't cut down on cost for accommodation as I wanted to stay in a decent place so my hotel costs about RM260 per night (Nox Boutique Hotel)..very nice room, not big but with tv, computer, jacuzzi, queen size bed, 5min walk to metro, lots of restaurants around..

for food wise, at least RM30 per person per meal (1 pax of pork belly for bbq is about 9000-12000won)..better to plan for higher to be safe even though if you order bibimbap it will be about 6000-7500 won at some places I went to..unless you want to cut cost for food, can go to their convenience store and buy cup noodles + their gimbap which is korean sushi, very nice way to save money  ..

when you arrive, straightaway go to a 7 eleven and get a T money card (for touch n go)..very convenient to use for public transport..its 1050won per entry to the subway minimum..i think if you pass a certain amount of stations then they will charge extra 100 as sometimes when i go far it adds 100..currently still in seoul until the 18th  ..btw anyone has experience entering those korean music shows as audience? not a big kpop fan as i was some years ago but still would like to attend just to watch as i'm free an easy

I just came back from Seoul a week ago. My style is a hybrid of both. Certain tour like visiting the DMZ (border) would require a local tour. Others you can take a taxi or subway and do it free and easy. With an elder, you may want to take more taxi. Anyway, zoom in on your interest, what you want to see, and go from there...

Enjoy your tour... Feel free to ask any questions and I am more than willing to share my experience as I was first timer too with my family.

Easy-lah. Just follow the guide on 1st page. The transport system there are so efficient. Anyway, if got elder following.. As in most DIY, required lotsa walking and even climbing the stairs of MRT stn stairs..So that part ..hmnn But DIY can be dirt cheap compare to tour. Most tour to Korea >RM3K. If you DIY wth Promo ticket, it is possible doing it even at ~RM1000-RM1500 per pax. for budget traveler 

The consideration that you need to factor is the proximity of your accommodation to Arex or Bus. Bear in mind if you were to take Arex then you still need to continue your trip either on foot, another train or even taxi. And there are technically 2 types of Arex - the Express version or the multiple stop version. In both cases, the end destination is the Seoul Station. Arex Express version (Right side if you are walking from the main terminal) cannot use TMoney and the multiple stop version (Left side if you are walking from the main terminal) can use TMoney.

Some Airport Limo (this is what they call the bus) have stops which are nearby to certain accommodation.

So ... it is not about cheaper or not. I'd advise to consider the distance of those stops to your accommodation.
Now there are travellers in here who would bring their folks who are elderly people. Please remember that Seoul and some parts of Korea are very hilly. It is very much different than in Malaysia where the buildings are built according to the shape of the geographical contours vs. Malaysia way of just cutting away the hills to make way for development. Almost all of their subways do not have escalator access from the main street. What does this means ? Some effort in walking is required.

I recommend those thinking to bring old folks to ensure they are fit to tackle the occasional hilly terrain and the many stairs. (Can very very steep in certain locations) Consider this ... back in the days where the tram up to the Namsan cable car was non existent, you could easily see elderly Korean walking up the steep hill (gradient of more than 50 degrees) without breaking a sweat or stopping. I'll stop here but you could figure out what I mean.