If you only have 3-4 nights in Dunedin, book this for your first night and have a contingency plan (another activity you could do in it's place) ready, so that if they cancel and move it to another day or refund you, you could try to catch it on another day before going home or do something else with the time, I wanted to see it so paid $450 to move my flights and $150 to add an extra night accommodation to try go see the stars but then the weather cancelled it and they refunded instead...
The night the weather was bad in Dunedin, it was good in every state of Australia and some other city in New Zealand and tonnes of amazing photos were posted on social media by others, just to rub our bad luck in haha
So definitely book for the first or second night of your trip, to try to have it moved to another night before you leave if you can in case of bad weather.