I recommend the Hokane trip.
A great day out which you can do all on one ticket from the central station in Tokyo.
You start with a suburban train out of the city, then transfer to a steep mountain railway with tunnels and sudden gorges, then to a very steep short train ride up to a viewpoint where you then take a funicular over a volcano and down to a large crater lake. if the weather is good you can explore here for a bit, then you take a pirate ship (honest!) across the lake where you are returned to the suburban train by a coach trip down a picturesque valley.

enjoy