Here's the free Wifi connection in Fukuoka.
This Wifi service has an alliance with Onsen Oita Wi-fi City (Oita, Beppu, Yufu). Once you register to either service, other one can be available without registration. NIshitetsu 100 yen Circle bus will join this alliance on September 1st.
Amu Plaza Hakata, Amu Est, and Hakata Deitos have common free Wifi. The service is available from 4:30 to 26:00.
Marinoa City has similar Wifi service to Canal City.