Summary
First of all: home of Kumamon. Lest we forget. Second of all: home to a lot of other things too.
Kumamoto Castle is the third largest in Japan and one of the most beautiful. The Yamaga onsen will soothe your weary travelin' bones. Eikokuji or 'The Ghost Temple' houses famous legends (some of which are spooky). And the Suizenji Gardens are considered one of the four best in Japan.
And don't forget Kumamon. I told you not to up top.