It's not necessary to register in New Zealand unless you are requiring a co.nz address.
I've registered three domain names... but only one in New Zealand. And in this case, my local host - IHUG (www.ihug.co.nz)- charged me a NZ$60 setup fee to process and a monthly NZ$10 fee to host the name on their server. I still had to pay the standard Internic (www.internic.net) domain name fee of US$70.00.
In another case, I registered a .com domain name and parked it with a United States host company at no charge. The standard Internic fee still applied of course, but was the only cost in the transaction.