You will always need an alternate when flying into Wellington ( part 121) no matter how good the weather ( single runway airport)
If you depart from a NZ airfield you don't need an alternate if the weather is beaut, if you depart from somewhere outside of NZ you do if the field only has one runway.
That is my understanding only, look into it more before taking off and getting into trouble! Remembering that all this is the minimum legal requirements and not neccesarily good airmanship. Personally I wouldn't want to arrive in Wellington without enough fuel to carry out a missed approach, go to Palmerston North and land with 1/4hr still up my sleeve.
Framer