In reply to snakebite: Go south for sure - lots of fantastic climbing to be had. Wanaka is a good base for peaks in the Aspiring Park including some of the more moderate summit routes.
Mount Cook region is where you'll find the concentration of big and generally more committing routes, and the most other climbers to hook up with (Unwin Hut is the Alpine Club base hut in Mount Cook Village).
Coming in from the West Coast either by heli or a long rough walk-in will give you a real adventure, and maybe a hot pool to unwind in if you're lucky!
Fiordland and the Darrans for true wilderness. Although climbing pretty much any peak in NZ is a mini (or not so mini) expedition due to the long valley walk-ins, simple huts - just bunks, maybe the odd pot and pan (or no huts) and lack of infrastructure. Basically you need to be pretty self-sufficient and cell phone coverage is minimal in the mountains of the south. That said, all of these things are kind of what makes it so special. No lifts, cafes on the mountains, and usually the place to yourself. Meeting other climbers on a route is often a cause for celebration and a chat as it's pretty rare most places!
Hitching is pretty easy in the south, otherwise cheap shuttle buses abound, but there aren't that many roads in the south and many climbing areas walk-ins begin at the end of long valley dirt roads, so wheels could be handy. Mount cook, you can pretty much base yourself in the village though and access from there.
Most gear is similar price to Europe apart from boots and rock shoes which are a lot more expensive.
http://alpineclub.org.nz/ for some general info.
Enjoy!
