ARC, the only airpark I'm really aware of in the same vein as the ones in the states is at North Shore Airfield about 35 minutes drive north of Auckland. I suggest you contact North Shore Aero Club about it. They have developed an area but I don't think anyone has built yet. It could be quite nice with palm trees being planted and a large stone entranceway etc.Not a bad area but not really paradise.
There is pauanui but I guess it is more likely to have pork at a jewish wedding than being able to get your hands on a house on the airstrip.
As for the North Island for climate....the weather is crap anywhere near Auckland....I would suggest Nelson at the tip of the South Island.