want to move from Tokyo to a small town, need suggestions

I'm a foreigner living in Tokyo with my wife. We want to relocate to a small Japanese town, but need help finding and picking the right one — I'm not sure how to start looking. My goals for the perfect place to live:

  1. Small, quiet, and peaceful– ideally with beautiful scenery that would lend itself to long walks or hikes. The "quiet" part is pretty important; the main reason for leaving Tokyo is the general noise of the city.
  2. Livable without a car (but we're happy to walk long distances!)
  3. Not warmer than Tokyo (similar temperature or colder would be fine).

I realize that my requirements are fairly generic, which means that I'll have too many options rather than too few. However, some specific suggestions would still be appreciated — I have to start looking somewhere!

Also, I work remotely, so that's not a factor.

by Meekro