I know you're not going to Fukuoka, but honestly, in Kyushu your best bet is Fukuoka, or to order online. I'm not saying there aren't little mom and pop shops still selling used cameras and film in any of the major cities, but unless you know someone who can point out the shop to you, it may be hard to find. I've been in many cities across different regions that, after a search online, yielded several possibilities of a shop or two selling film, and I have wasted up to a day chasing down those shops only to find that they were all closed and abandoned (something the internet/google maps does not update well). It would have been better to order straight from Yodobashi. My Japanese is terrible, but I navigate the site using google translate, and I have been able to order a lot that way. It usually arrives the next day, or for special items, within 2 or 3 days.
Most cities have a Kitamura Camera and IF they sell film, in all likelihood it will be various flavours of Fuji colour neg. That's it. No slides, no black and white, nothing bigger than 35mm. Actually, that would be true of some supermarkets and/or convenience stores - there may be a few 3-packs of Fuji colour neg, but that's a big if.
In any event, I hope you enjoy your trip!