Hakone

Hakone is about ninety minutes from Shinjuku on the private Odakyu line, which makes it the least effortful detour on the whole Tokaido corridor. It is a caldera full of hot springs, and the reason to stop is a single night in a ryokan: a bath, a long dinner, an early morning, and back on the rail line the next day. Two nights is usually one more than the area sustains unless you are walking.

The area is laid out as a loop rather than a town — train, then cable car, then ropeway over the sulphur vents at Owakudani, then a boat across Lake Ashi, then a bus. It works, and it is scenic, but it is also a sequence of transfers with queues at each one, so start it early or reverse it to travel against the day-trip flow. If you are only crossing the caldera once, individual tickets often beat the combined loop pass.

Two things are worth confirming before you pay for the ryokan. Dinner is normally tied to a fixed arrival window, and arriving late can mean losing a meal you have already been charged for. And some baths still refuse guests with visible tattoos, though private family baths are a common workaround — ask directly rather than hoping. As for Mount Fuji: it is visible from the lake on clear days, mostly in the colder months, and completely absent behind cloud on many others.