Avoid winter and summer, unless you're visiting Hokkaido in summer or Kyushu in winter.

The seasons here are wicked.

Once you have some japanese friends you will

have an interesting time anywhere in the country ..

there are temples and archaeological sites everywhere in japan

and plenty of solitude too, esp in hokkaido...

I would avoid holiday weeks like Golden Week, everything is booked up.

if you are on the quieter side, then Tokyo or large cities might not be for you. even Kyoto is not all that quiet.

if you enjoy nature, go away from major cities. one (and rather typical) idea might be to go to Shinshu region. there is a nice town called Matsumoto in the middle of mountains. several creative type Gaijin live there, from what i heard. ocean side by fishing town would be quiet as well. there are so many places.

my personal dream (because i am not familiar myself) is to explore the Sanyo region, which faces Setonaikai (or Setouchi Sea). prefectures in the region include Hyogo, Okayama, Hiroshima and Yamaguchi. if you like cold Hokkaido or Tohoku. if you like warm, Sanyo, Shikoku, Kyushu or even Okinawa.

hmmm... it is really about the damn time for me to explore the country side of Japan myself!

I just returned from Japan and if you are wanting quiet, you might want to avoid Osaka. I was there for a little bit and it is a full city...amazing and wonderful and I would highly recommend it (the food is AMAZING!), but not if you want more quiet.

I also spent about seven days on the southern island, Kyushu in a little town called Kannawa. It's near Beppu which is right on the northern tip of Kyushu. It's a lovely little town and everyone is extremely friendly. There are thousands of onsen (natural volcanic hot springs) in that area so it's definitely a wonderful place to relax and because a lot of people in the area don't have showers or tubs, the onsen are more about community bathing, so you really become fully enveloped in the culture there. But it's beautiful and there are moutains around there (mountains everywhere really) so you can get some hiking in too.

Koyasan (Mount Koya) might be another nice place that's a bit more quiet. It's on Honshu about an hour and half away from Osaka and is up in the mountains. It's home to many old temples and graveyards and increibly beautiful! The most beautiful forest I've ever been in. And you can stay up there too and stay in one of the temples (I didn't do that, but would like to when I go back).

I moved around Japan with a native from Osaka so that did make everything much easier as far as understaing more of everything and getting around more smoothly. But pretty much everyone I encountered was really nice and helpful, so that's a plus. Try to learn some of the language (if you don't already know it) before you go, at least the basics because that helped me (even though I was with someone that could speak it).

Hope that helps...