Hi Maureen, no Auckland Hospital does not provide wifi.
I especially bought the IPad with wifi plus 3G. So it has a card in it like your smartphone does and I buy internet use. 3G per month, when we need it.
If you intend to just use your smartphone perhaps you could update your data plan for the month that you will need it. So you will use your data plan to download while you are in hospital.
I'm sure either Vodafone or Telecome will assist you.
Tammy