Kirk here. In looking for some sort of information about Kumamoto on the web I happened to find this website. It has quite a lot of information about onsen in Kumamoto -- not just what you see in this picture. It also has a page of information about tatoo-friendly establishment, including several onsen in Kumamoto.
By the way, I've been to the onsen in the photo on the lower right. This unique spot is in Manganji, in the Oguni area. You undress and bathe without privacy -- men and women together. I think it's a vestige of traditional Japanese bathing customs.
The 10 Onsens You Should Visit in Kumamoto — THE ONSEN MAGAZINE
We've selected the 10 best onsens in Kumamoto. If you are planning to visit Kumamoto, read this article to know must-go onsens there!