Queenstown is currently served by Air New Zealand with regular direct and connecting flights from all major centres. You can fly direct from Sydney year round with Air New Zealand International and in the winter additional flights operate directly from Brisbane.
Qantas also flies direct from Sydney and Brisbane during the winter.
Do fly into Queenstown. The last leg of our journey was from Christchurch to Queenstown. It was a clear day and we were able to follow the journey all the way with our map, and an added bonus was that the pilot gave a running commentary: "...and over there you can see Mount Cook, the highest...".
The approach to Queenstown airport is interesting too. You bank round the mountains and can see the lake ahead. The final run in brings the port wing-tip apparently within feet of the mountain-side. It has to be one of the most spectacular landings since the closure of the old Hong Kong airport (from my experience I also recommend Nice, France and Hewanorra, St Lucia).
The terminal has recently been upgraded to accept international flights and it quite smart, with a small selection of shops and refreshments. We were easily able to pick up our hire car.
Air New Zealand has the most service to Queenstown. They fly to and from many cities within New Zealand. Most international flights will pass through Christchurch or Auckland.