The most popular place in town for foreigners (and cool Japanese!) to hang out was Xelha's a bar/restaurant/nightspot in the heart of Kokura.
See http://www.ne.jp/asahi/kitakyushu/nightlife/restrnts.htm for more information on other places to go in Kitakyushu.
Kurosaki!I've been here a few times and I enjoyed being here at every time.
It has many kinds of places. Like, Japanese Izakaya's, Pachinko Parlours, Snacks, Karaoke places.
One of my favourite bars is King Kong. They make great cocktails!