In the unlikely event that the Soviets would go after New Zealand, there's the consideration that New Zealand was no longer a US ally after 1985.
But if this was the Protect & Survive timeline, New Zealand would still be an ally of the USA. As such, both Auckland and Christchurch would be important targets had the Soviets chose to attack them with the MR-UR-100 or UR-100N ICBM's, with the ICBM's based in eastern Siberia near the Trans-Siberian Railroad.