The aquarium is Marine World Uminonakamichi. Hakata to Kashii is 11 minutes and Kashii to Uminonakamichi 20, plus the airport subway, transfers and the walk.
The Domestic Terminal connects to the subway; International Terminal arrivals need the shuttle first. Then pick a Hakata, Tenjin or Nishijin handoff for Momochi.
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.