Yeah, I remembered where you were.
So if you stick around long enough, the mountains and fjordlands to the west of you will keep getting taller as the uplift caused by plate subduction outpaces erosion. Of course, that will be a problem for you, on the coast. New rivers will form, great, braided rivers - a new Yukon, an Eagle... Not a big deal, at least for a few million years, since you're on pretty high ground, but eventually the center of the island will tilt and deform, west dipping east, and you might have to relocate a couple of times so as to avoid being deposited into the sea.
The fun stuff comes maybe 10-20 million years from now as the subducted crust melts a couple hundred miles or so off the west coast of the South Island (and many miles down). The magmatic activity increases, the magma intrudes toward the sea bed and volcanos are born - a new Hawaii bursting through the surface. If there's enough juice in the magma chamber, the erosional deposition fills the ever-narrowing channel between the South Island and NEW Zealand and something like a new Australia is born. In its depositional basins are lots of precious metals precipitated to the surface by hydrothermal action. Stake your claims now. :)
The geological map of the South Island reveals one curiosity for dinner parties - Dunedin, proper, is something of an upstart as neighborhoods go. South of Dunedin the sandstones and siltstones that comprise the country rock are all Cretaceous - Jurassic and Triassic - but Dunedin itself is basaltic - intrusive in some spots, pyroclastic in others - and dates only as far back as the mid-Eocene. When you drive into town, you're driving about 30 million years forward in time.
