Auckland is the main airport for incoming flights to New Zealand. Like most, it is quite a distance from the city centre. It is best not to cycle into the city unless you have a particular reason. There are few accessible cycle paths and fewer signposts. Auckland city traffic is not always kind to cyclists, there are several shuttle buses, with cycle racks, available to take you to city accommodation.
Buy a mini map at the airport. They are cheap and helpful guides for Auckland city. You should also pick up a free Backpacker/Hostel guide. If you wish to avoid the city and cycle south, then there is a good camping park at Ramarama.
Backpackers can obtain a brochure listing hostels, etc throughout New Zealand at the tourist centre at the airport. Some of the hostels provide camping facilities. The government runs a number of basic, cheap campgrounds, usually in picturesque rural surroundings. The best guide for cycling in New Zealand are two small books (one for the north island and one for the south) called Pedallers' Paradise by Nigel Rushton which lists routes and hill profiles and local information in an easy to read, cheap guide (approx. 12.00 N.Z.). See his site www.paradise-press.co.nz - this lists stockists in USA, Canada, UK, Australia, Holland, Germany, Scandinavia, Switzerland, Belgium and New Zealand. Buy the books before leaving because they have limited availability in New Zealand.