Kokura is the beating heart of Kitakyushu — the district with the castle, the covered arcades, and most of the places worth eating and drinking. It's where you'll want to base yourself.
The covered shopping arcades are among the longest in Japan and thoroughly disorienting — a labyrinth of shops, pachinko parlours, and restaurants stretching in every direction. The Uomachi Gintengai Arcade is the spine of the system. Don't rely on landmarks to navigate; bring a sense of direction or accept getting pleasantly lost. Kokura Castle, rebuilt in 1959, sits at the edge of the arcade district and is worth the climb for the views, with the Matsumoto Seicho Memorial Museum and the postmodern Riverwalk Kitakyushu complex right next to it.
Kokura is small enough to explore entirely on foot. The buzz in the streets is real — this is a city that actually uses its city centre, unlike many Japanese towns of similar size.