Erm...
2 April :
Tokyo(fr Odawara)- Hakone(Hakone Shrine,Lake Ashi sightseeing cruise,& Owakudani) - Lake Kawaguchi(want to try onsen)
Considering if you take romancecar:
- 7:00am: Leave Shinjuku (not factoring time you need to reach Shinjuku from your hotel)
- 8:40am: Arrive Hakone Yumoto
- 8:40am to 9:40am: Hakone Yumoto to Moto Hakone by bus (35mins travel, 20mins waiting for bus)
- 9:40am to 11:30am: Hakone Shrine
- 11:30am to 12:00nn: Lake Ashi Cruise (timetable:
http://www.hakone-kankosen.co.jp/foreign/en/timesheet/index.html)
- 12:00nn to 12:30pm: Togendai to Owakudani
- 12:30pm to 1:30pm: Owakudani
- 1:30pm to 2:00pm: Owakudani to Souzan
You would possibly be done with everything by 2 and have half a day to try Onsen. It's possible but it seems a little rush, and this is not including anything you may want to do on the way, that are covered in the round course.
- Is it possible for us to make it one-day trip? As above, its possible if thats the only 3 things you want to see. But if not, do make extra time for other things as well. I would not advise rushing in Hakone, especially if you're going to rush off to Kawaguchi, and then on top of that Kyoto.
- Do u have any suggestions for us to choose a nice place to try private onsen? If you're asking about Hakone, in April I'm not sure if its already fully booked, I previously booked a private onsen at Hakone Yuryo - you can ask your Tokyo hotel to do the booking for you, that's what I did.
- In your opinion, better we spend the night in Lake Kawaguchi or Kyoto? (our next trip is Kyoto) Sorry! Can't answer this I have no idea but I don't think Lake Kawaguchi is along the way to Kyoto - I could be wrong. Kyoto's pretty accessible from Odawara, which isn't far from Hakone Yumoto.
Hope this answers at least some questions? :D