Hakone (day trip / overnight) is a real time commitment — fit it in only if it's a priority.
Allow Full day / overnight.
A scenic loop by mountain railway, ropeway, pirate ship and onsen, with Fuji floating over Lake Ashi on a clear day — the classic relaxing escape, best as an overnight at a ryokan. The catches are real: it's much better with a clear day (Fuji hides often), the loop is a transport puzzle, and as a rushed day trip it's a lot of transit for the payoff.