Fukuoka and Hakata were twin towns until 1889, when one municipality took the castle town's name. Hakata is now third largest of the city's seven wards.
Airport Line to Hakata, then Nishitetsu bus 46 or 99 to Hakata Futoh (Bayside Place). International Terminal arrivals need the shuttle to the subway first.
Yakuin-odori Exit 2, then a short bus or about 15 minutes on foot. Last entry is 16:30, so a late landing decides whether the zoo still works that day.
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.