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Did a flight to NZ once with Korean Air. It was the cheapest flight I could find and included a 1 night stay in a 4 star hotel in Seoul on the way over. That was nice. Have to say, Korean Air had the best in flight food I've ever had also, some nice bib bim bap.
The other flight I did to NZ was via LA one way and San Fran on the way back. The LA transfer was hell, took 3 hours to get through customs. then had to collect luggage and check it back in and through security again to get back on the same damn plane. It took up the whole 7 hour layover.
The way back was better for a 12 hour stop in SF. Arrived in the mornings spent the day site seeing, riding the cable car, seeing pier 39 and the sealions etc.
That used to be a nice stopover location ... not so sure the city has quite the same vibe now.
That said, Doha or Dubai is the shortest route to OZ. Massively so. So if you're planning direct, that;s the way to do it. I did go via Singapore before but that meant an 8 hour layover in the airport plus an increase of in-air flight duration by 4 hours or so