Prefecture with cheap apartments

Currently planning on going to Japan to teach for a year. Looking for a very affordable prefecture to stay in, one where rent is not too high, somewhat rural but still present the opportunity to experience all that Japan has to offer, in terms of food, festivals and culture, etc.

So like... all of them.

Basically, every prefecture (yes even Tokyo although it can be hard to find!) has more "rural" areas outside the big cities that you can find good deals on apartments/living expenses.

My advice: look around this website and decide on a general area (example: Hokkaido; Tohoku; Kanto; Hokuriku/Chubu; Kansai; Chugoku; Shikoku; Kyushu; Okinawa) that sounds the most interesting to you. Then, look for a job in that overarching area. I recommend looking outside big cities but still on major/semi-major train lines to make travel easier.

Food/Festivals/Culture you can find anywhere.

Two things to be careful about concerning "rural" areas:
1. Cost of public transportation is more expensive than cities.
2. The deeper you go, the less job opportunities.

Basically, every prefecture (yes even Tokyo although it can be hard to find!) has more "rural" areas outside the big cities

No, it's extremely easy to find rural areas in the prefecture of Tokyo. You can even get lost in the mountains of Okutama. And yes, transportation can cost you more and jobs can be less in those places, even in Tokyo.

Another trick is to look for places further from train stations. You can commute by bus, shop in supermarkets and still save housing fee, even within the 23 wards of Tokyo.