Get out of the city and in to nature!
Don't stay in the city. You can find charming little places right outside of the city. Mt Eden is BEAUTIFUL, Ponsonby is lovely as well. And it's easy to get back in if you want to. Explore the culture by visiting museum and galleries - Auckland is up to date and know what their doing. And get out! Strap on your hiking shoes and walk up Mt Eden and One Tree Hill. There's a lovely little stroll from Auckland domain to the city. Lovers' walk start and stop there as well.
Insider Tip:Mt Eden, Auckland Museum, Auckland Art Gallery, One Tree Hill, Wallace Art center and Wintergarden. Golden Dawn is a hidden but wonderful place in Ponsonby. You find the Best burger at Degree by the Viaduct! Bus or walking is a great (and cheap) way of getting around. Countdown is the supermarket for backpackers.