This article is from the New Zealand FAQ, by Phil Stuart-Jones and Lin Nah with numerous contributions by others.
A brief summary of entry requirements can be found at
B4.5.1 Departure Tax
A departure tax of $NZ20 per person (over 5 years old) is charged of people
leaving New Zealand who have been in the country more than 24 hours. This
is to be paid after the traveller has checked in as the tax receipt is
attached to the traveller's boarding pass.
No vaccination certificates are required to enter New Zealand, but if
illness occurs within three weeks of entering the country, consult a doctor.
Facilities are good but not free to non NZ residents (except in the event
of injury due to an accident). Please refer to this page for advice
regarding Health and General Insurance: