I stayed for one night in Toyo Hotel, which is very close to Hakata Station in the heart of Fukuoka. Easy to get to the airport and Shinkansen as well as local city destinations. Check in was a breeze, room was waiting, and clean conditions. The only 'meh' is the comfort of the bed, but this is standard in Japan....the beds are way too firm for my liking. Not Toyo Hotel's fault by any means if all hotels are like this.
Check out next day was also easy with a quick drop of the key and out the door. The price was exceptional at under 4500 Yen, or about $43!
Definitely recommend for a short stay in Fukuoka.