Kochi has a laid-back, subtropical atmosphere and a wonderful castle.
Busan (for the 24 hours I was there) struck me as being a heady combination of ultramodern, almost futuristic architecture and infrastructure with a substratum of Old Asia.
I didn't see much of Fukuoka, except for staying overnight before boarding the hydrofoil to Busan and having coffee with a professional contact, but any guidebook will be full of suggestions.