There are some great areas to enjoy both hiking and onsen in Japan. I can recommend the following ones:
is one of the nicest wild but still reachable area of Japanese Alps; there is a great hike going from Kamikochi to Hida-Takayama, and there are some of the nicest rotenburo in Hida-Takayama.
is one of the most active volcanic area on Tohoku; you can hike from Tamagawa Onsen (the most acidic onsen in Japan) to Goshogake Onsen, and further to Hachimantai; probably a multi-day hike, see also the Lonely Planet Hiking in Japan and this JNTO pamphlet
- In the same area, Nyuto Onsen is also a great small village which is at the beginning of several hikes.
- Not sure of the hikes, but Numajiri Onsen
is not really an onsen, it is in fact a river made from hot spring water!
- Northern is also the Aomori prefecture, with very attractive onsen - check Secret Onsen
web site; I am not well-aware of hikes there, having been there mostly in winter, but I heard there are some nice options.
- Easier hikes, closer to Tokyo - and mostly in forests - can be found in Okuniku
. I like the area, onsen are nice, but it is much less wild than options above.
- Izu offers great onsen, and hiking there is supposed to be nice, but I am not familiar with it, neither.
Hope this will give you some ideas