Ohorikoen Station for the lake, Tojinmachi as the alternative, both about seven minutes on foot. The Art Museum inside the park has its own access and closing time.
Do not aim for a vague riverside promenade. Nakasu Riverfront is the target, and the yatai hours decide whether you arrive for the evening or the daytime version.
Airport Line to Hakata, Nanakuma Line to Watanabe-dori, then about three minutes on foot. A Nishitetsu bus to the Yanagibashi stop is the official alternative.
Not on the Airport Line. Change at Hakata to the Nanakuma Line and get off at Ropponmatsu, Exit 3. The Dome Theater schedule decides whether the visit works.