Ok, well what are your starting and ending points? Are you thinking of going hiking at all? Are you going to drive around the whole South Island in two weeks?
Here are some things to start:
http://en.wikipedia.org/wiki/The_CatlinsThe Catlin Coast is this rugged kind of uninhabited place that is actually really cool. A lot of time will be spent on gravel roads, but that is OK because it will be a rental and you have insurance for these things. The area is beautiful and they have some rare wildlife there and a petrified forest on the coast and NEAT.
Lake Tekapo is on the way from Christchurch to Queenstown (and everyone goes somewhere around here). Do not miss it, because it has the most amazing colour that never seems to come out the same in photos and is truly breathtaking.
DEFINITELY go to the Milford Sound. Definitely go hiking somewhere in Fiordland National Park (yes we spell it fiord, because we are special) and DONT go swimming in Lake Teanau because that shit is always cold. Oh and bring bug spray and pet a Kea for me (they are the parrots that eat sheep and destroy cars).
Rizzo mentioned Akaroa, and if you are in Christchurch then it is totally worth it to drive over the hills to visit. It is a really stunning bay area and you can go and check out Hectors Dolphins (they are tiny and endangered and cute).
Dunedin is the Scottish city of New Zealand! You should visit it because that in itself is kind of silly and you can buy tartan and people that far South talk kinda funny (even more so in Invercargill though). Also it is full of very drunk students who light things on fire constantly.
While you are in Dunedin it would be silly NOT to check out the Otago peninsula where you can visit the Royal Albatross Sanctuary and watch big honkin' birds do birdy things. There is also probably the only castle ever in New Zealand there (which is ok I guess), but better than that is the Yellow Eyed Penguin Conservation reserve where you can stalk yellow-eyed penguins when they come in to nest from a super days fishing. You get to hide in trenches with binoculars and just you know, watch 'em. It is really fun!
http://www.otago-peninsula.co.nz/http://en.wikipedia.org/wiki/Yellow-eyed_PenguinOk that is just the bottom bit of the South Island. And not even all the good stuff, so you really need to pick and choose I guess! More to come including: big mountains, sandy beaches, rocks shaped like pancakes and my personal favourite WHALES.