In my various drunken sprawls around the downtown kumamoto area, I'd have to say bar days is the coolest bar found yet. Kind of a rock grungy feel to it, but if you're into music this is the place to be cos it has around 1000 cd's lining the walls.
Reading the other comments, sanctuary is no doubt a cheap place to get a drink, but it's also a little on the grimy side so don't expect too much if you go there. However, it's open late and isn't that hard to find, so it may be worth a shot if there's nothing else going on.
The following website has heaps of kumamoto bar and club reviews, which you may find useful: http://www.kumavibe.com.
Dress Code: Anything goes.
A honky tonk isn't exactly what you would expect to find in southern Japan. But the owner, Charlie Nagatani, makes sure everyone has a good time listening to him play the sound he fell in love with as a kid. I think he's more Texan than I am.