Here are some short jogging trails if you happen to be visiting Kyushu. Although many people take the bus between Beppu Station and the Kannawa-area Jigoku, they miss out on the park between the two areas, complete with paved running trail:
Map, running in Beppu
Kokura's path isn't quite as useful. Situated around Kokura-jo just northwest of the station, the running trail loops around the castle and Japanese garden. Rather than using that path, you should run alongside the inlet - it's a beautiful riverwalk, passing sports parks, and interesting bridge designs.
Map, running in Kokura