The notion of New Zealand being nuked is a tireless joke around here. Even considering the premise of a Fallout universe, NZ's involvement in an armed exchange between China and the US should be akin to the Korea War. Unlike Australia who boast a more considerable military and could potentially aid the US with its uranium supplies, all NZ can offer is a small detachment that would not have contribute much threat to the PLA by themselves. Besides, the minute Washington goes silent from the Great War, Wellington will cease all military actions against China, since there's no way NZ can take part in an overseas theater on their own. Therefore, there really is not a single strong reason to send a nuke to NZ, unless they're interested in mutating our sheep.
Hypothetically speaking, if I were in charge of nuclear weapons resources for a US that is engaged in a war with China, NZ would be pretty close to the top of my "strategically important" countries. Bomb-laden planes, missiles, etc. coming from NZ would not only be approaching from a different angle, but would also be arriving much sooner than the bulk of the ordnance.
Again, hypothetically speaking, if I were in charge of selecting targets for a China engaged in war with the US - any US-friendly countries within a certain range (whatever the range for the most accurate missiles) would be pretty much a no-brainer.
Sorry New Zealand, in the Fallout Universe, you're probably also a radioactive wasteland.