Kaitaia Airport is part of the Bay of Islands airports (together with the airport near Kerikeri) but this is the smaller one. From Kaitaia Airport Air New Zealand operates one or two daily flights to Auckland International Airport. Facilities are pretty much non-existent: don't expect shops, an ATM or cafes at this airport.
All transportation options from Kaitaia Airport should be booked in advance, before your flight. Taxis can be booked as well as a rental car.