You want to become a NZ citizen, I want to become an U.S citizen. I can see a solution here....
But realistically, residency gets you everything you need. You don't gain much by getting citizenship.
For park skiing, Cardrona, Remarkables, and Snow park are definitely the places you want to be. Wanaka and Queenstown are super fun towns to live in too, lots of skiers and partying to be had at either.
Christchurch/Canterbury has some sick big mtn terrain but not much in the way of park. It's actually a city, unlike Wanaka/Queenstown.