Fukuoka is unbelievably urban, with two city centers (Hakata and Tenjin) despite having quite a rich feudal part. Most of the feudal heritage was torn down in the Meiji era in the 19th century. Heritage-wise, all that's really preserved are innumerable shrines with deep significance to the city's and Japan's history. Most of the best ones are in the Gion area.
The city really appreciates its green spaces. It has a plethora of parks, the crowning jewel of which is Ohori, closely followed by Maizuru and Nishi. All of these are really beautiful in springtime, during cherry blossom season. The beaches along the harbourside are fun, but not spectacular. There are a couple of attractive islands offshore that you can access by ferry.
There's a lot of shopping to do. A good percentage of city's main attractions are incredible shopping areas, malls and arcades. Nightlife is good, but there's no one single bar or pub or club that is objectively great.
If there's anything at all in the things to do that really sets Fukuoka apart, it's the food. The city's cuisine is phenomenal, and if a traveller happened to arrange their itinerary around the best way to eat their way through the city, they'd likely have an incredible experience.