In Kokura Minami there is an awesome area called Hiraodai which is full of Limestone Rocks (they kind of look like sheep grazing).
Hiraodai Park is Japan's best example of a karst plateau formation, 22 square kilometers in area and rising 400 to 600 meters above sea level, providing views of the surrounding mountains.
The park is a landscape of hills and mountains dotted with pure white limestone, a super example of karst deposits. It also contains quiet and beautiful forests, a meditative waterfall, and the Ojika and Senbutsu Shonyudo stalactite caves which cost 800 yen to enter.
We walked back from the Kanmon Bridge just as the sun began to go down. Very pleasant places to sit and view the strait on route.
Also in Kokura Minami this waterfall has a little temple nearby.
In summer it is possible to bathe in the cool water. You can get here by Nishitetsu bus but by personal car would be best.