Oboke and Iya area, in Miyoshi, are good places for trekking and viewing the real nature. You can also take the boat tour (or do kayaking) on the rivers along the gorges.
The area includes also some special places, such as the Vine bridges. Not something for the person with freight of heights.
Another odd experience is to find the small village, where there are more scare crows than inhabitants.
How to get there
The best thing is to rent a car and drive. Very difficult to get around otherwise.