The Bone People by Keri Hulme (1984) — Set on the South Island's West Coast but essential reading for understanding New Zealand: its Maori-Pakeha tensions, its coastal isolation, its violence and tenderness. It won the Booker Prize and remains the most internationally recognised New Zealand novel.
Mister Pip by Lloyd Jones (2006) — A Bougainville Islands story by a New Zealand writer, but it captures something about the Pacific world that Auckland is part of. The novel was shortlisted for the Booker and is accessible and moving.
The Penguin History of New Zealand by Michael King (2003) — Not a novel, but if you want to understand what you're looking at — the volcanic landscape, the Maori place names, the colonial architecture — this is the clearest single account of how New Zealand became what it is. King was one of New Zealand's finest historians before his death in 2004.
Once Were Warriors by Alan Duff (1990) — A brutal and unflinching novel set in South Auckland's state housing estates. The film adaptation (1994) brought international attention; the book is harder but more complete. It is uncomfortable reading, which is rather the point.