Henry Creek Campsite is a sweet spot nestled in Fiordland National Park, near Lake Te Anau on the road to Milford Sound. There are about 30 non-powered/tent sites, which are first-come first-serve. It's 15 US$ per person and you put your cash in the box provided on the campsite. Besides a public toilet, there aren't any facilities. It's a short walk to the beach, from where you can see some amazing sunset views over Te Anau Lake.
In our experience, the campsite isn't too busy so you can enter quite late and still find a spot!