On our entire trip, Queenstown was the one place that felt touristy. It's a backpackers haven, with a condensed town filled with food, activities, and people. As such, a great option for lodging is the YHA Queenstown Central, party of the YHA New Zealand group. They offer perks for worldwide members, so be sure to ask. This facility is nicer than a typical hostel, with private room and private bathroom options. Once you get past the checkin desk and sparse lobby, it feels like a hotel.
Our room was clean, and even had a view of the lake. The restroom was spacious and very modern. There isn't much in the way of amenities here, it's just a cheap, safe, and clean place to stay. They do not have elevators, so be ready to carry your luggage. We had some issues with noise as our room was below the common kitchen area, which despite being closed, was cleaned early morning.
More than anything, this place is convenient to everything worth doing in town. For people venturing outside of the town, Uber is the easiest bet. There airport shuttles to/from the Frankton Airport just a 15 minute drive down the road. The Skyline is also just a quick walk away. We'd stay here again!