I’ll give you a good tip for travel in Japan outside the main centres. Get a car! This may sound obvious, but anywhere that doesn’t have a decent transport system is going to be too much hassle without one.
Japan is famous for its trains, most notably the bullet train and things like the Yamanote line in Tokyo, but outside major centres, the public transport is average at best. Having a car gives you the freedom you want to travel on your own schedule, and is more likely closer to how the locals get around.
Of course this comes with a number of considerations, like ensuring you have an international license, and you may not be able to get in touch with the locals as much as you want, but you can do this in other ways. You might want to be sure to stay at places run by the people there (as opposed to things like AirBNB), and to also make frequent stops at shops and things 🙂