Hello @worldtravaler, great question! Our stateside auto insurance policy doesn't provide any coverage in New Zealand. Coverage for non-owned vehicles is only provided in the U.S., U.S. Possession or Territories, Puerto Rico, Canada and limited coverage in Mexico. Therefore, I like to recommend you purchase coverage from the rental agency.
For more information about coverage for rented vehicles, just enter "Rented Vehicles" in the Search bar on top of this page.
Please let me know if you have any additional questions and hope you have a safe, wonderful trip! Thank you for choosing USAA! ~ Stacy K.