If transiting the same day, will be possible to remain airside if interlining of the bags is allowed, both Air NZ and UA are * Alliance members, so interlining is most likely possible (not guarenteed).
As mentioned a Visa is needed if you go landside, if you do choose this there are lockers for hire at the Coach(Bus) terminal under Central station, if you just want to dump the bags.
Alternativly just across from Central station there iare two a YHA Backpackers hostels.