I live in wellington nz i grew up here and have traveled most of nz. I would have to say the best places to go are:
(taupo and rotorua) for extreme sports sky diving/bungy jumping/ zorbing/ white water rafting etc and the good thing is all of these are well priced compared to doing them in other countries
There is also a lot of thermal activity here like boiling hot mud pools/ natural hot water pool you can swim in and a lot of history. there is also a volcano you can snow board on between june-november about an hour away from taupo.
auckland for the city life iv never really liked it.
wellington where i live great for a couple of days/great night life and cafe culture there are heaps of free thing to do and great scenary. No point in staying to long tho.
Queenstown- extreme sports/great scenary its the most expensive town in nz but still cheap compared to a european city.
scenary from lord of the rings was filmed all over nz so you will get to se a lot of it. The best think about it is every thing is so cheap a full meal will only set you back $2.5-5 us or 2-3 pounds. transport is very cheap but not domestic flights. hostels are cheap they hardly go over $15 us a night.
hope this helps good luck with your travel