There are all sorts of options from the lap of luxury down to the cheapest ryokan. Ask at the Information desk, third floor of Kokura station.
2-14-2 asano (north of kokura station), tel. +81-93-5311121, (http://www.rihga.com/fkokura/). the top hotel in town and the only rihga royal hotel in kyushu.
I had a place for Â¥33,000 monthly, only needed to pay Â¥5,000 for change of locks, Â¥3,500 matinance and Â¥1,600 for Internet. Not wifi, so if you want it, you need ever a cable to connect your laptop or buy a wifi router.
They have an English price list, and you can find monthly on the bottom of the sheet.