If your flights go to or from Auckland, you could take the Overlander train.
Price: $129 each way
One service daily - takes 12 hours. Leaves 7.25am, arrives 7.20/7.25pm.
The train includes a buffet car and (usually) an observation car with a massive picture window at the rear. The route is frequently listed as one of the most scenic train journeys in the world - see http://www.seat61.com/Overlander.htm.
List your name if you are interested in taking the train, to find others who are too (and share taxis etc at either end).