The South Island is by far the most spectacular, and with only 17 days here, in total, it's going to be cramming things in to really see the country. However, I usually recommend the following places to people.
In the North Island...
about 4 hours North of Auckland (by car) are the beautiful Bay of Islands, and then there is the Coromandel Peninsular (South East of Auckland by several hours), Rotorua, is three hours south of Auckland, and you would detour through there on the way to Wellington and the Cook Straight ferry. With 5 days in Auckland (WHY???) you'll have used up the first week just getting that far. So if you had more time... add Bay of Islands and Coromandel, otherwise head for the South Island. (Both the aforementioned could be done as overnight trips out of Auckland, because there's not much to bother seeing in Auckland itself, when the rest of the country is on your doorstep. However, in Auckland... must sees... driving up the volcanic cones of One Tree Hill and Mt Eden for spectacular views. A ferry crossing to Devonport... or further afield to Waiheke Island. A visit to Kelly Tarltons and drive along "the waterfront" and a walk around the Viaduct Basin. That's two days.... max.

Wellington has Ti Papa Museum, so if you can get there in time to see that before crossing the Cook Straight it may well be worth it, depending on your interests.

In the South Island I'd suggest driving the Kaikoura Coast to Christchurch (one night) and from there heading inland to Lakes Tekapo, Lake Pukaki and into Mount Cook (one night). From there, it's on to Queenstown, home of the bungy jump and Skipper's Canyon, the Remarkables (mountain) and some other fantastic tourist stuff. Three nights there then through to Lake Te Anau (glow worm caves) and onto Milford Sound via the Homer Tunnel. That's the highlights of NZ covered really, (lots more, but you just don't have the time to take in the West Coast and the Fox and Franz Josef Glaciers) and you can come back to Christchurch any number of ways, perhaps to Invercargill, the Catlins, Dunedin to Christchurch and dump your vehicle there to fly out internationally.

Our cities are nothing to write home about. (Hamilton and Dunedin are places I'd pass through, in the main, and not stop in). You live in one of the most beautiful countries in the world architecturally, so what you want to concentrate on here is our natural isolated beauty, and getting to know the people of New Zealand.


Hope that's some help.