The whole reason I went to Christchurch was to take the TranzAlpine Train across the middle of the south island. I didn't hear about this incredible train until I met Viktor (typical).
Viktor and I got up early and had the YMCA Hostel call us a taxi to get to the rail station. When we made our reservations, we requested to be seated on the right side of the train. My mom, an avid TripAdvisor searcher, found a comment saying that if you sit on the right side of the train when going from Christchurch to Greymouth and the left side of the train when going the other way, you don't even have to leave your seat to get the best views.
Let's just say, even though I took Mama Max's advice (thanks, Mom), I was on the windowless observation deck 60% of the time.
(See why below)
The whole price of the TranzAlpine Train was about NZ$140. It is a bit pricey just for transportation. However, I've come to find that transportation, whether it's by bus or train, is also an excursion. The views you get by traveling on the ground in this country are incredible, especially on the south island.
Don't just fly. Take 2 short months out of your life and really experience New Zealand. Rent a car or campervan! Buy an Intercity Flexi Pass! Take the TranzAlpine Train! Anything that'll keep you on the ground while exploring.