Go wine tasting on Waiheke Island. Waiheke is home to some fantastic wines and has some of the best beaches in the area. Can get crowded during the weekends, but very quiet during the week. It seems a world away from Auckland, but is only 35 minutes by ferry.
On your way through the Waitakere Ranges, head to the little beachside village of Piha and be prepared for stunning natural beauty.
Rotorua, Hamilton, Waitomo Caves and Taupo are all within several hours drive and all have a lot to offer.