Moanalua Gardens is a landscaped historic park in west Honolulu, best known for the huge monkeypod called the Hitachi Tree. The grounds also include a small cottage associated with Prince Lot Kamehameha, who later became Kamehameha V.
This is a calm stop rather than a blockbuster sight. It is most useful if you are exploring beyond Waikiki and downtown, or if you want a quieter green space with a bit of Hawaiian royal history attached.