There are so many wonderful places to go to in the North Island of New Zealand. My favorite beach close to Auckland is Tawharanui which is in a marine park. I love to walk there and the beach is nice too. http://www.doc.govt.nz/conservation/marine-and-coa...
My favorite beach further down the island is Papamoa beach which is near Tauranga.
Further off the coast is a bird sanctuary on Tiritirimatangi (locals call it Tiri) and it's a fantastic day trip from just north of Auckland. The island is being regenerated with native trees and repopulated with birds. The bird song on the island is deafening and visitors can get up close to the birds and see them in their natural habitat. http://www.tiritirimatangi.org.nz/.
Rotorua is a very firm favorite with locals and visitors alike with its boiling mud pools, geysers and hot springs.
These are just some of my favorite places in New Zealand. The list is long though!