Fukuoka is a city in Japan.
Sue PA is easily accessible through cheap public transportation. It is located 20km east of the city center at these GPS coordinates 33.587619, 130.499784. It is not a very big PA but if you are riding east, you can also stop incoming traffic. You can use the bus or Kashii Line and stop at Suecho Station. From Hakata Station, you will need to take Sasaguri Line and transfer at Chojabaru to access Kashii Line, It should cost you 280 yens. From Suecho station, it is a 500m walk.
Experience from user Savvyhitcher: I went there in June 2018 to go to Hiroshima starting from Fukuoka. The lady working at the Sue PA helped me make a sign in japanese. The PA is rather small and has little traffic, but within 10 minutes I had a lift with a driver offering to bring me to the next Service Area. The driver was laughing and joking as he was surprised to see a westerner hitchhiking at such as small PA. I think it is a great spot to start a journey from Fukuoka. I got to Hiroshima within the same day.