We just returned from a wonderful month in New Zealand--our third trip--and spent roughly two weeks on each island. It was not enough time, really. Since it's your first trip, I would recommend flying into Christchurch on the South Island and spending your time on that island only--you can do the North Island next trip (you will want to go back!). Spend a couple of nights in Christchurch, three or four in Wanaka (where you can take an unforgettable plane ride to Milford Sound and also visit Mount Cook Park). (Make Queenstown a day trip if you must see it--it's gotten terribly touristy and packed with tour buses).
Then head over the Haast Pass and drive up the West Coast to see the Franz Josef glacier and Pancake Rocks, cut over to Motueka and/or Nelson to see the fabulous coastline of Abel Tasman Park, drive two hours east to the Marlborough Sounds area for a couple of nights near Picton or Havelock, then down via Kaikoura on the east coast back to Christchurch.
I'm not sure how that works out time-wise, but you'll see some of the best sights in the whole country. We are partial to the top of the North Island, too, from the Bay of Plenty and the Coromandel and past Auckland up to Northland, but you won't have time for that, too in just 12 days). Driving is easy.