Day 1: Hakata and Nakasu
Morning Kushida and Yanagibashi, afternoon Canal City, one yatai at night.
Day 2: Dazaifu
Nishitetsu from Tenjin. One umegae, the Tenmangu, then either the museum or Mount Homan.
Day 3: sea or west
Dusk at Fukuoka Tower, or sunset in Itoshima. Not both.