Aucklander here - agree that Auckland's nothing special, but did you check out the west coast black sand surf beaches such as Piha, Karekare, and Muriwai? I think there's a couple of surf schools at Piha. To get there you drive through the Waitakere ranges, which have hundreds of kilometres of bush trails. Also out there is a fresh-water lake in the middle of remote sand dunes, quite a walk but refreshing on a hot day - Bethells Lake aka Lake Wainamu.
EDIT: Bear in mind west coast beaches often have big waves and strong rips, so only swim where there is a surf patrol, between the flags. If you prefer safe white sand swimming beaches, try Auckland's north shore (East Coast Bays), especially Long Bay Beach. An hour or so north of Auckland, Te Arai Point is one of the nicest unspoiled white sand beaches IMHO.
Also a lot of people like to visit Waiheke Island in the Hauraki Gulf, with its wineries. Rangitoto Island is Auckland's youngest volcano at about 600 years. (If you want to visit a live volcano go down to White Island in the Bay of Plenty.)
Bay of Islands is pretty. Way up north, check out Ninety Mile Beach (you used to be able to drive down it at low tide, not sure if that's still the case) and Cape Reinga at the northern tip of the north island. Be mindful the far north of NZ is a bit of a high crime area.
Coromandel Peninsula is very scenic, though attractions like Hot Water Beach can get very busy in January. Bear in mind very narrow windy roads. There's a day tramp you can do right up the top of the peninsula, near Port Charles (from Stony Bay I think). There's a company that will drop you off at one end and pick you up at the other.
You can catch the ski lifts up Mount Ruapehu in summer I believe, but make sure you go on a nice clear day so you can enjoy the view. Ohakune is a nice little ski village at the base with plenty of accommodation. Tongariro National Park is a popular place (try the Tongariro crossing walk if you're fit, see Mount Ngauruhoe aka Mt Doom).
Speaking of LOTR, Matamata has Hobbiton but I recall it was ridiculously expensive.
Rotorua is probably worth seeing as Gizmo said, though when I took my American friend there she turned her nose up and called it "stinky town" (though she was a NYC girl). Lake Taupo is quite nice, and there are some jetboat tourist attractions nearby which are quite fun.
Waitomo Caves are quite cool, miles of caves and more glow worms.
Wellington's Te Papa museum is good. Wellington is a nicer, more friendly city than Auckland IMHO, though colder and windier. Just north of Wellington is the Kapiti Coast, and I think you can get tours out to Kapiti Island, a nature reserve.
That's about all I can think of off the top of my head.