The person you need to ask is Ian Wilson.
Back when I was last in NZ, the local track (Pukehoke) was open every Tuesday/Thursday for open lapping for NZ$40. Often I'd get in over 100 laps, usually limited by the amount of fuel I'd bring along. I'm sure at least the price has gone up by now.
Do a search for Pukehoke Park, Hampton Downs, Taupo and Manfield, which are the North Island tracks. Hampton Downs is under contruction, and looks like a very nice track. Taupo has just been extended for the A1GP, and again is a nice track. Pukehoke has been on the verge of closing down for at least 10 years. Manfield is a little further but worth trying out.
Some advice - don't exceed the speed limit by more than 3-5 kph. There are lots of cops with laser & radar, plus fixed and mobile speed cameras. After a while you'll get to know how they operate so when you see an abandonded van beside the motorway you'll realize that it contains a speed camera.
I used to drive to Wanganui for work. At one point on the way there is a sign "winding road next 122 km" but it is actually about 140 km of continous corner/small straight/corner combinations. The brakes on the company car never lasted very long.