One of the more interesting things we did when visiting New Zealand was go to Stewart Island. south of the South Island. All through our trip we'd tell locals "We're going to Stewart Island" and they'd say "really? I've never been there". It's a tiny place, about 400 permanent residents.
Stewart Island has retained most of its unique endogenous life. Ulva Island was outstanding, a small nature refuge with lush forests and odd birds. There are hiking trails all over the island, too, seemed like a great place for a ten day trek.
I love remote places like this. There's something very comforting about the quiet, the odd collection of people, the knowledge that there's not much to do. I enjoy being in places like this, and I enjoy knowing I'll be leaving again in a couple of days.
PS: if you're thinking of visiting, do yourself a favour and take the plane. Even the locals say the ferry crossing is awfully rough.