In reply to Removed Usermountbeckworth:
My favourite bit of adventure is Mount Myogi near Tokyo (bus from for day trip or stay hotspring hotel base of mountain) Its a caldera and you climb literally on the knife edge ridge above fantastic forest. I wrote a report on it .
http://www.mountain-forecast.com/peaks/Myogi-San
Good stop over going towards Nagano / Mount Asama (also good)
I also like the Izu peninsula, but its not mountains, just very pleasant volcanic/coastal landscape with loads of hotspring resorts/beaches.
Have fun