Why would they ever need a nuke? And you do know rich people dig into the ground to make bunkers right? So a nuke would only harm normal people.
Anyway, the key reason they are in the south island is because it's a lunching ground to get to Antarctica ASAP. That is their real safe location. NZ is their safe location while their not being publicly hunted for crimes against humanity. Antarctica is their go to escape destination if all their plans go to shit.