Are there any SIM cards with unlimited internet access available in New Zealand, for a stay period of 3 weeks?
Vodaphone counter at Auckland Airport don't offer any unlimited bundles, and I wonder if there are any available in Christchurch.
This is NZ we're talking about. It's still lagging with a smaller population in terms of technology up-take and bandwidth capacity.
As such, currently, there are no unlimited data plans in NZ for mobile phones (Orcon has introduced them for broadband internet at home). Why? You can read the whole discussion about what might be required for this to happen on NZ's GeekZone site.
The best you're going to be able to do, as a friend did earlier this month, is the $19 plans for 500MB from 2degrees, Vodafone or Telecom. I'd recommend 2degrees IF staying in the cities - I used it in Christchurch in Oct/Nov this year, however if you're going outside the major cities, Vodafone may be a better bet as they have much better coverage.
Enjoy Christchurch, it's my home town! :)