Hi,
I'll start with the caveat that I've never tried to move money to NZ.
What that said, I have had to move money between the US and Canada.
I've been relatively happy with XETrade (
http://www.xe.com/xetrade/). Their exchange rates are good, or at least better than the banks and fairly close to spot when you are talking about larger transactions.
At least between Canada and the US, all the transfers can be done by electronic transfers so no need for wire fees.
If there exist companies that are listed on both the NZ and an American stock exchange, you can look into "Norbert's Gambit". This essentially involves buying the same stock on one exchange, journaling it over to the other currency equivilent, and then selling it in the currency you want. I haven't had as much experience with this, but if it works for you, you can get extremely good exchange rates.