I LOVE Queenstown and can't say enough good things about it.. It's a real tourist mecca though.. so that can be a bit overwhelming, I think you definately need to check it out though.
(Anyone correct me if I'm wrong I may be a bit biased) I think the South Island is far better in terms of skifields and there's more of them.
Hostels for $5.. I don't think so.. but you'd be looking at anywhere from $25 - $50NZ for cheap accomidation.. Or even I'd recommend hiring a campervan and just travelling around.. The south islands small enough to do that.. and if you're coming all that way you may as well see the whole country.