Fritz, great photos. I am still figuring out where to stay in the mountains near Tokyo. I want things to do. Relaxing, nature-y stuff. Maybe I should just stay in the city again and day trip out to the mountains?
Check out Nikko. There is a national park with plenty of hikes, at least two onsen villages with Yumoto and Chuzenji and Nikko itself with the World Heritage Site.
Another Option would probably be Hakone, but I havent been.
The further from Tokyo and the deeper into the alps the more scenic and tranquil it will probably get but it will also be a lot more time consuming.