Sanzao Airport. There are taxis from Zhongzhu Building to the airport for 20 yuan. You can also take bus 207 to Gongbei and get off at the terminal station for 6 yuan. There are quite a lot of open spaces, and the area near the entrance is relatively empty. Also, the view from the nearby mountains is also good.
There is an airport in Kyushu Port that seems to be a heliport used by the military.