Hakone is only 1h from Tokyo, maybe a bit more, but you can enjoy the romance car (special train) and you won't feel it' s far at all...
Ashino is one of the most beautiful lakes I've ever seen. You can see the Mount Fuji, eat onsen egg, have a wonderful view from the hotels, those are on the bottom of the mountains... many many onsens... real onsen!
They also have the Picasso museum in Hakone. It is very interesting, with sculptures and different painting you never see in the museums.
The transportation is good, with ships, roapways, trains, cable cars and buses those can take you everywhere in Hakone!
