The anchor stone from Maui’s canoe (Maori legend) is definitely worth a visit. It has over 85% conservation land and has only a small human population – mostly fisherman – who live mostly clustered around the township of Oban (which has the island’s only pub and is also well worth a visit). There is only 20km of road. A large part of the island is a bird sanctuary with all introduced predators removed (rats and cats mainly) so the bird life is amazing and is a lot like New Zealand would have been before human settlement. The first settlers were whalers in the 1830s and there are some cool ruins from this early settlement, which can be seen on a number of the well signposted walks.
Accommodation can be an issue on the island so make sure that you book in your Stray Mate app before you go.
Travel across the Foveaux Strait on the Real Journeys express catamarans from Bluff. The captain will give commentary about the interesting landmarks in the area and there's free tea and coffee on board to enjoy during the 1hour crossing.
If you're also doing the Milford Sound cruise, Real Journeys offer a special combo deal for Stray passengers where you can get the Stewart Island ferry and Milford Sound cruise for a special rate!
Book this in the 'Te Anau' destination of your Stray Mate app.