If you have 1 week to spend, definitely fly to Christchurch and drive to Queenstown. Did this a couple of years ago and it was a beautiful drive, once you turn a bend and the rows of trees disappear/open up to mountain peaks and lakes is a great sight. Take your time driving down, i think we stayed the night at Mt Sommers & Omarama.
Sample itinerary could be something like this:
Day 1 Arrive - checkout Christchurch
Day 2 Drive to Mt Sommers find something to do during the day, we did this
Off Road Dirt Bike Quad Bike Tour South Island NZ | Adventure Trail Rides (for the kids?)
Day 3 Visit Lake Tekapo + Mt Cook. Stay at Omarama
Day 4 Head to Queenstown via Lake Wanaka. On the way, we stumble on this which was really cool (i dont have photos on me)
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National Transport & Toy Museum Wanaka, NZ – One of the world's largest private collections of aircraft, vehicles and toys. (HUGE collections of toys, cars, planes, etc)
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Warbirds and Wheels Museum Wanaka - Warbirds and Wheels Museum & Diner (there's a 1950's style diner here for lunch? )
- There's also a brewery but i forgot the name.
Day 5 Queenstown
Day 6 Queenstown
Day 7 Queenstown
Fly home ...or extend your trip and go to Auckland+Rotorua
Multiple snowfields within 1hour of queenstown. There's plenty to do here and take in the scenery from your hotel by the lake.