Air New Zealand has regular flights from the main centres. Alternatively fly into Christchurch on a cheaper flight via Air New Zealand or Jetstar and roadtrip down to Dunedin.
Jetstar now has direct flights from Auckland to Dunedin.
Dunedin airport is located 20 minutes out of Dunedin City. Door to door shuttles costing approximately $25-35 will bring you into town. More information.
Note: Dunedin is a small city and it does not take that long to get from A to B. Travel from the North end of Dunedin to the venue is 10 minutes by car.