I never made it to Wings over Wanaka when I was there but several co-workers went and raved about it. If you're in Wanaka already and it's summer the Blue Pools are a nice hike and cold swim, both worth the trip.
I didn't spend much time on the North Island, but I can recommend the mud baths in Rotorua and a tour of Hobbiton was much more intereting than I, not a fan of the books or movies, expected. Beaches to the north are nice and isolated, and at Hot Water Beach (east coast, west of Auckland) you can rent a shovel and dig your own geothermal hot tub on the beach.
On the South Island, where I spent a fair bit of time, Queenstown has all kinds of adventure tourism if you're looking for bungee jumping or skydiving or jetboats and the like. The approach and departure into Queenstown airport is "interesting." If you want to stick to aviation, I highly recommend the Grand Traverse tour of the Southern Alps and Mount Cook with Air Safaris in Tekapo, a small town kind of halfway between Christchurch and Queenstown. I believe they also operate out of Glentanner if you want to be closer to Mt. Cook. +1 for
@kyleb's suggestion of a Milford Sound boat tour, or anyplace around Fjordland for that matter. My favorite thing to do when I had a long weekend was bolt to Akaroa, a little "French" village built in a caldera on the east coast east of Christchurch, and just wander around the town, eat seafood, and sleep. Christchurch can be fun and has some history to it if you're into that kind of thing. It's got a great walking downtown. The best thing I did there was stumble onto the annual Big Band festival and just spent the weekend walking from place to place listening to excellent music.
I've got lots of suggestions and opinions, but that's enough for now.
Nauga,
stranger in a strange land