You can go to Tenjin on foot. Nearest is Akasaka Station, 13 mins from the airport. 7mins to Hakata station. 13 mins to Canal City Hakata. 2mins walk to the closest bus stop.
There are many restaurants and select shops. There is a 24 hours supermarket next to our apartment. Don Quijote is also walking distance from our place.
There is a rental bike shop near my room,so you can also enjoy cycling. Ohori Park, Fukuoka Castle Ruins are close to our place. I recommend you to take a walk there.