It’s been a dozen years, so my answer is a little dated. But it’s maybe an 11 hour flight from LA. I don’t remember exactly because we went there on the way home from Oz. Back then, anyway, QANTAS, Air New Zealand, and United were the most likely options. And, at least then, United was a FAR distant third place in terms of service, flight attendant attitude, etc… We had great experiences on both QANTAS and ANZ. YMMV.
We flew into Christchurch (from Oz) which is on the South Island. We flew home to LA from Auckland which is on the North Island.
I’d just hop on Expedia and start looking…