Film is still readily available (35mm and 120, at least here in Wellington), but it will cost quite a bit more than back in the US. Bring it with you, just keep it in your hand carry and you'll be fine. You can sometimes find reasonable deals on the local auction site (www.trademe.co.nz). E-6 development is expensive.
Near Auckland, you've got the islands in the Hauraki Gulf that are worth a visit. A little further afield, you could head over to the Coromandel.
If you've got the use of a car, and a week or so, the options are many.