The AKL lounge is great. Nice breakfast, showers, computers, tv, magazines, etc. Even can iron fresh shirt if you want.

The quiet room is no more though, now a childrens room. However if you grab a comfy couch round the back it may not be too noisy for a doze.

BTW when are you flying? If you fly LAX-AKL on NZ1 (777 a/c) arrives 5:30am. The first flight to SYD is 7:00am and the second 9:00am. Factor in transit security and boarding times and will only have 3 hours in the lounge for the latter flight, 1 hour for the former.

The 767 is of course old business class, but comfy enough for short flight. If my schedule allows (rarely the case) I prefer the later flight since the early morning rush at SYD is over by then - the first flight runs into huge queues at immigration, and quarantine (x-ray).