Soldato
...
You might be able to do a day trip to Hakone as there are things to do besides the onsens. There is a cable car up to caldera and you can ride on a pirate ship across the lake.
I think I've done the cable car there twice and both time the visibility was so poor (due to the weather) that you could barely make out the other side of the caldera let alone anything else.
I haven't done very well with view in Japan at all ... I've been 5 times now and I have seen My Fuji exactly once (from the train last time). I've been plenty of places where you are supposed to be able to see it but what with haze and low clouds it wasn't visible ...