Did not know that Air New Zealand had Zeds, but I am with Expressjet, so maybe we do not have the agreement. So, if you can get out to HNL, you can non-rev off Hawaiian, or go to Sydney, then ZED off Qantas. Problem with Sydney is getting a visa just to clear customs. I actually bought a roundtrip ticket from LAX to Christchurch (I was going to by a Auckland to Christchurch ticket anyway) and it was not too bad. Air New Zealand is awesome to fly on, non-rev or revenue.
If you already have an itinerary, then you probably cannot go wrong. If you have 14+ days there, I would recommend 2/3 of the days exploring the south island and 1/3 on the north. You cannot go wrong with anything in NZ, but feel free to PM me and I can give you some highlights that I ran into.
Best trip I have ever taken, and I have been taking trips for over 16 years. Have fun!