I've toured there on three separate occasions, with a total of about 4,000 miles logged on those steep hills and rugged coasts. First, although it's expensive, you can have a reasonably priced experience by camping out.
Lighthouses always offer a good spot nearby, and it's hard to beat Japanese beaches.
Most towns, large or small, have a river running through or by them, and along those rivers there is inevitable a park or ballfield, or croquet court, and nobody seems to care if you camp there. In smaller towns, the city park, if it's on the coast or near a wood, is also good. The funny thing is that the Japanese don't pay much attention to a Gaijin over there. Don't do things which will draw too much attention, and don't set up camp until evening. These covered pavillions have a table, and many have running water too.