I haven't lived in Invercargill. I lived in Mosgiel, 15 minutes west of Dunedin, +-5 hours drive away from Invercargill, part of the Otago Province. I did visit there in Autumn. It is a lovely area. It is colder. The Autumn evenings are cold enough to warrant using a winter coat outside. During the day it was really warm, unless you were at Bluff, which is closest to Steward Island, and like most of the SI it is windy. The SI falls into the Roaring Forties, so there is little chance of no wind, there is always wind, the strength differs from day to day.
I think it would be a good way into the country, you can always move around when you find something in a different area.
Good luck with the application!!