NZ has the best regular economy product across the Pacific. NZ flies to SYD, MEL and PER (via AKL) and has flights from LAX, SFO, YVR and HNL to AKL thus plenty of choices. NZ also has flights to other places in Australia - ADL, OOL, BNE, and CNS.

Premium awards (on any airline) on this route are very hard to get - typically need to be booked as soon as they are released (ie 11 months before departure).