Auckland: Biggest city in N.Z, 1.2 million people. Transport is expensive and difficult to use. Accommodation is about 1/3 more expensive than elsewhere. However the there is a lot to do and see.
Hamilton: About 200,000 people in Hamilton, 1 hour drive to Auckland and Auckland Int Airport, Has an International airport of its own. Comparitively cheap. Transport really easy to use, easy to get around. Quite a bit to see and do if you know where to look.
Wellington: Capital, Parliament sits in Wellington, about 300-400 thousand people if I remember correctly. International airport. Not sure about transport but I know there is a bus service.
Christchurch: About 500,000 people. Totalled by a large earthquake. Do not go to Christchurch.
Dunedin: About 200-300 thousand people. Can be very cold, snows in winter. Lincoln University, similar to other centres although isolated from other cities.