If you're going to stay in Queenstown then your closest option is Coronet Peak, which is about 20 mins away from town.  Coronet has some really fun natural terrain and pretty decent lifts, but no park and it can get quite crowded. Check out www.nzski.com
The Remarkables is 45 minutes away, is way less crowded and has sick terrain, but you have to hike a bit to get to the really good stuff. The park is sweet, but there's no pipe. It also gets loads of sun because it's North facing (It works opposite in the Southern Hemisphere).  www.nzski.com
Cardrona is sweet, it's about an hour away from Queenstown, 30 mins from Wanaka.  Really good park and it has a 22ft pipe, but there's not much terrain, it's pretty flat, and it gets really crowded. www.cardrona.com
Snow Park is awesome, it's about the same distance from Queenstown and Wanaka as Cardrona is but way less crowded then Cardies, i.e. no punters.  It's got a really fun setup this year, nice pipe, jump line and tons of jibs but nothing else to ski.  It's also open for night riding on Tuesdays, Fridays and Saturdays. www.snowparknz.com
Treble Cone is really sick.  Really steep, fun terrain; gullies, bowls, chutes, drops and stuff.  But there's pretty much no park and lift tickets can be quite expensive, but a way around this is to get a rental car from Juicy rentals (Free lift pass at TC with any rental) but it's about 2 hours from Queenstown and 45 minutes away from Wanaka.  www.treblecone.com
Pretty much all the backpacker accom is about the same price and facilities, and everyone hitches here, I normally have to join a queue of hitchers to get home.  If you're only going to stay for a few weeks, then you should try to get to as many places as you can because they've all got something different to offer, I like Remarks though, it's got a nice mix of everything.