The Hoomaluhia Botanical Garden is located in Kaneohe on the windward coast of Oahu. This garden, at over 400 acres, can be explored by car, bike or on foot (recommended). The flora of a diverse set of tropical regions are represented her, including Africa, India, Polynesia, and Tropical America. On the grounds of the garden there is also a picnic facility, a campground, and a nice lake (but no swimming is allowed). All in all, it's a great place to bring the whole family.
And, by the way, Hoomaluhia is the Hawaiian word for "to make a place of peace and tranquility", so bear that in mind before honking your horn.