If you don't want to do outdoor activities, consider these:-Fukuoka: The largest city in Kyushu, lots of shopping
-Dazaifu: Near Fukuoka but has more cultural sites, like shrines and temples
-Beppu: If you like hot springs, this is one of the most famous cities for it. The "hells" sound quite interesting, too.
You could also try Shimabara (near Nagasaki) or Kumamoto.