There are many restaurants and bars in Fukuoka but I found a good wine bar which you can do wine tasting with inexpensive cost.
This place is called Au Bord d’Eau Fukuoka located just right next to Nakasu and Nakagawa river.
5 kinds of wine and sparkling costs only 1400yen.
The view from the window is beautiful and I am sure that you will enjoy tasting of wines!