New Zealand's national museum sits on the waterfront and is free to enter. The permanent collections cover Maori culture, natural history, and New Zealand art. The earthquake house simulates a real quake, and the colossal squid specimen is one of very few in the world. Allow at least half a day — there is a lot here, and it is well presented.
Te Papa Tongarewa
Free national museum with Maori taonga and a colossal squid