Historic and laid-back, Matsuyama is Kyushu's biggest city. It's top sights are Matsuyama Castle and the Dogo Onsen Honkan, the oldest hot spring in Japan. Good off-the-beaten track destination, but hot-spring suburb of Dogo is slightly popular as a hot spring resort with Japanese.
Dogo Onsen and Dogo Beer Main Store are worth seeing.
Hot spring and train trip
Daohou Hot Spring