Auckland city has many good dealer galleries and our public Art Gallery is worth a visit as is the Museum in the Domain.
Early morning or late afternoon walks in nearby One Tree hill (also known as Cornwall Park) are a must. It is a working farm and the Information centre there gives you some of the early history of Auckland.
Ferries to the stunning islands of the Hauraki Gulf leave from the bottom of town and are easily accessible using the bus at the top of my street on Mt Eden Road. I strongly recommend the island called Tiri Tiri Matangi, it is a bird sanctuary teaming with New Zealand native birds. Waiheke Island is glorious for vineyards, restaurants beautiful beaches good swimming and bush walks. Try Onetangi beach for swimming.
The Waitakere Ranges are have of many of my favourite bush walks and views of the Tasman sea from this wild west coast. See the several urban and other Auckland walks books in my study.
Auckland is also a great place to depart for day trips. Try the Coromandle Peninsula, Rotorua, famous for its geothermal activity, and review the many brochures I have left in the spare bedroom.