Queenstown's a very lovely place with lots of activities but not sure if you can try all of the activities with only US$50 a day.

Get up to Queenstown Hill and take in a paranomic view of the whole town, then Luge down the hill.

One of the other things I tried was to rent a car/4 wheel drive and make a day trip to Glenorchy. The scenery there is fabulicious - quiet, contemplative and full of snow-capped mountains. There are many unsealed roads to explore. Get info from the Visitor Centre in the Glenorchy "town centre" for maps etc. You will drive past farms of furry highland cows, waterfalls, more snowcapped mountains and gravel roads with streams running through them. There are also places to hike and there was one where I saw some "ghostly trees" - actually some algae or fungus that grow on tree branches creating a ghostly effect coupled with the fact that there were very few human beings around. Quite surreal. Best thing about these activities is that they are free except for the car rental. And oh yes, pack your own lunch/snacks/drinks before you go. There's not as much choice in Glenorchy. In the mountain roads, even less (you can't eat the cows).

I understand part of Lords of the Ring was filmed around these parts. Enjoy!

well, since you are in queenstown you have GOT to try parabungeeing. its the coolest ever. but expensive.
if you need any information about queenstown try the "justqueenstown.co.nz" website. it has everything from culture to nightlife to food to places to stay... basically everything. it really helped me plan my trip.
have fun!!!