Te Papa Museum is a must. This is the new museum representing New Zealand's history, culture, geography and art. The country is relatively young, but the history is fascinating, from the Moioris and the Moaris through to modern European immigrants. There are great displays about the geology, including a reconstruction of an earthquake. A corrugated iron car caught my eye - yes they really do make them! The artwork is beautiful, from ceramics and sculpture through to fine art and glasswork.
Coffee shops abound, and the interactive displays are great for all the family.
Quick Tips:
If you fancy a swift pint, there's no shortage of watering holes from the sports pubs (if you don't like rugby, avoid them) through to old fasioned lounges and trendy wine bars. Most cafes serve alcohol too.
Best Way To Get Around:
If you have a car, drive up Mount Victoria to get your bearings and see the view, then find a downtown car park to dump it in. Then walk. A good little trip is the cable car up the hill. While you're up there, have a walk round the botanic gardens - very picturesque. Then get a bus down to the harbour side for a sit down and a cup of tea!