tardtasticx: This should help you. Contact details for all public hospitals in the country, organised by DHB.
So you would count North Shore Hospital and Waitakare Hospital, both under the Waitemata DHB.
Auckland City Hospital and Starship Hospital (Paediatric ED, not sure if this counts but its 24/7), both under the Auckland DHB.
And finally Middlemore Hospital in South Auckland under the Counties Manukau DHB.
Hope that helps, those are all the ones listed in auckland and that sounds about right too,
Cheers, just the sort of public list I was after. I had a poke around the MoH website but all i could see was data on ED wait times