I am not being clear. Why live in an NZ city of 200,000 when you could live in an American one of the same size and enjoy a lower cost of living, and cheaper rent?
Portland, Oregon might be the closest counterexample that comes to mind, but it is an order of magnitude bigger — population of the greater metropolitan area is 2.4 million.
There is a fair amount of inexpensive housing here but not in areas with the same cultural values. (Perhaps Wellingotn wasn't the best example, but it's in the only NZ city I've been to firsthand.)
Feel free to shoot me an email (in profile) if you'd like to discuss more.