Lessening the distance between the US and New Zealand can only be a good thing. We should remember who has stood with us in the past and do what we can to encourage them to do so in the future.
I think the US should just let this issue drop about no-nukes in NZ. It is a very hard arguement to make that we don't want nukes in Iran or North Korea but we would set NZ aside because they don't want them. Granted, New Zealand is not a nation given to terrorism, but I think you can get my point nontheless.
"Do not forget your dogs of war, your big guns, which are the most-to-be respected arguments of the rights of kings."
- Frederick the Great, King of Prussia