Yes — Hakone is the most varied day trip near Tokyo: a volcanic valley, a lake with a shrine torii, an art museum and a hot-spring soak, all in one loop about 85 minutes out. The caveats: Fuji is weather-dependent, and the lake clogs with tour groups by late morning. Go clockwise, start early, and it delivers.
Yes — onsen, Fuji views, a volcanic valley and a scenic loop make it the most varied easy day trip from Tokyo. Just go early and clockwise, and check the forecast if Fuji is your main goal.
Hakone for onsen and Fuji views; Nikko for grand shrines and waterfalls. For a relaxing soak near Tokyo, Hakone wins.
Yes for the classic loop. Stay overnight only if you want a proper ryokan onsen and a slower pace.