QUOTE(captivesim @ Aug 28 2019, 08:29 PM)
Where would be more convenient to stay? shinjuku, shibuya or tokyo station? plan to go Gala yuzawa, Kusatsu , Hakone day trip. any value or budget hotel to recommend? not too far from train station. 15 minwalk max
For me, Shinjuku ftw, We stayed in Tokyu Stay Yotsuya for 14 nights. Larger than usual hotel rooms, has a kitchenette and washing mc which is a bonus! No room service and room cleaning is once a week. There is a station (Yotsuya) nearby, 5 minutes by foot. Four lines pass through this station so it is very convenient. It is away from the busy tourist areas but enough restaurants, snack and convenient stores. Shinjuku main station is 3 stops away, but be aware that it is a very huge multi-level station (reputed to be the largest in the world). It is always busy, rush hour is a nightmare. We got to Hakone using Odakyu from Shinjuku station. We also did the so called Hakone Loop which covers Gora, Mt Fuji, Lake Ashi etc. Mt Fuji is really worth it and should be considered as part of your trip to Hakone. Make sure the weather is nice, i.e. not cloudly or worst rainy. Mt Fuji can be very shy,lol.
Shibuya, I find more suited for young crowd and a bit chaotic as it is close to Harajuku (another 'young' ppl place). Tokyo station is a bit out of the way but most Shinkansen leave from here!
To be fair, any of the areas you mention is really good and as long as you are near the metro, everything else is ok. Tokyo, I think has one of the best of not the best metro network. Take a little time to study the rail map and you will be ok. The three lines I use most of the time to travel around Tokyo are the Red, Marunochi Line, the Yello Ginza line and the very useful but busy Green Yamanote Loop. Good luck!