Administrative Head Office for Fukuoka Prefecture. There is quite a good view of the east of the city from the top.
Best way from Tenjin is on the subway, get off at Chiyokencho-guchi on the Kaizuka line. Leave the station at exit 6 and keep going, with the road on your left. Take the first right and you will see the park. If you come from hakata, you can take the JR Sasaguri line to Yoshizuka. The park entrance is pretty much opposite the station.
5 min from Chiyo-kencho-guchi st'n on foot.
(Sasaguri line) 5 min from Yoshizuka st'n on foot.