@wakemantk For buying both cars from dealer and second hand private cars - look at Trade Me
https://www.trademe.co.nz/
Another spot to look is Turners Car. They instantly buy and sell cars.
Especially - when you are leaving. They will buy your car on the spot - the whole deal is done and you get your money transferred to your bank account in less than hour.
https://www.turners.co.nz/
In terms of paying - I would recommend a bank account. The best was to get one - would be through Wise - they are a international money transfer company and they will transfer your US dollars a lot cheaper than a bank. They will also give you a nz bank account (without any of the hassles of a local bank).
https://wise.com/nz/
In NZ, most large money transfers are complete via bank transfer - you just need someone bank account number to complete the money transfer.