Fiordland (like S.W. Tasmania and Patagonia) on the S.E. corner of the South Island is astonishingly unvisited. For good reason.
… Fiordland National Park, which has an area of 12,120 square kilometres, making it the largest national park in New Zealand and one of the larger parks in the world. Most of Fiordland is dominated by the Southern Alps and its ocean-flooded, steep western valleys. Situated within Fiordland are Browne Falls and Sutherland Falls, which rank among the tallest waterfalls in the world.
The name “Fiordland” comes from the now-common variant of the Norwegian word “fjord”. Fiordland features a number of fiords often misnamed sounds, of which Milford Sound is the most famous, though Doubtful Sound is even larger and has more and longer branches.
Fiordland has few human inhabitants and is the least-populated area of New Zealand … and many areas almost inaccessible except by boat or air. Te Anau township, the only larger settlement close by, has under 2,000 permanent habitants, though it boasts around 3,000 tourist beds.
This region is ideal for those who are looking for a real trekking challenge. (The sandflies alone were enough to drive me off.)
An article called Hidden Valleys of Fiordland, a bushwhack to George Sound, may be enough to scare you off, as well:
It all began on the shores of Lake Te Anau at a pessimistic looking information sign. The town of Te Anau is shown to sit in a rain shadow, with an average rainfall exceeding that of the legendary Milford Sound. We then knew the full extent of what to expect, as one trip member, John, put it “This is possibly the wettest trip we could attempt, except maybe a traverse of the lake bed!”
Fiordland is drenched. Even the well established hikes (Hollyford, Kepler, Routeburn, Milford, etc.) are challenging in the rain.
Choose a more remote track — Doubtful Sound and Dusky Sound would be our first choices — and you are up for a memorable trip.
Te Anau area hikes – Dept. of Conservation
Doubtful Sound – original – flickr
besthike.com 
Muddled thinking by your correspondent: Te anau sits in a rain shadow, but this means it’s on the dry side of the hills. Milford gets 300 to 400 inches annually, and Te anau gets roughly 50. It’s a prime example of rain on the windward side of hills (the west in this case) and drier weather in their lee.
Hi, The Dusky track is a great Tramp. I had the pleasure of doing it in 1986. I came off the Routeburn and team up with a Swiss couple. If you think the dusky is wet you should try Stewart Island. Te Anau is my favorate town in N.Z. I was first there in 1974 when did the Milford and the Routeburn for the first time. N.Z. a great place and a wonderful place to Trek.