Hi and welcome to SaleHoo, Daniel :)
I think it would be best to register your business based on your location. To register a business in the US you will need a US address. I don't see any added benefits of you register you business in the US as well...
You can still source your products and even sell within the US (via dropshipping) even if your business is registered in your home country.
Should you decide to register your business in NZ, you might find this guide helpful - Link hidden: Login to view
All the best!