I’ve been to Fukuoka in April 2018. The city is pretty wheelchair-accessible. Most of the sights like Ohori Park, Dazaifu Tenman-gu Shinto Shrine and Fukuoka Tower are fully wheelchair-accessible.
The beautiful Uminonakamichi Seaside Park is wheelchair-accessible, too. However, the JR Kashii Line train line, unfortunately, isn’t accessible to wheelchair users. There is no wheelchair-accessible wagon and the step is huge. Too huge to put a ramp. My husband had to lift me with my manual wheelchair to get on board. This was the only negative point during 4 days in Fukuoka.