With a resident population around 30,000, Queenstown is actually a small city, meaning that you'll not find too many boroughs or niches where grabbing a drink or an authentic bite to eat are both authentic and widespread (unless you've got a friend in town who will cook you genuine South Island lobster or clams). The good news is that due to Queenstown's huge adventure-tourism bend there are a ton of central places to grab a bite or drink.
You'll find that the large majority of establishments are centered around the Queenstown Mall, a short pedestrian thoroughfare near the Queenstown Gardens and the shores of Lake Wakapitu. The six blocks or so from Shotover Street to Earl Street are so packed with options and locals and tourists who regularly pursue them that it will be hard not to find a good time or a good meal day or night. As far as food goes, the Fergburger on Shotover has a deserved reputation for big and tasty sandwiches for any time the craving hits you (well, until 5am). Winnie's in the Mall is also hugely popular until late, meaning that a wait for a meal may get pretty ridiculous. Still, there'll be music and dancing once the evening rolls out on the weekends, so you can actually enjoy the crowd. There are a handful of decent Thai places, some quality coffee joints (Vudu Cafe & Larder tops a lot of lists, but gets really packed), and even a seafood restaurant that prides itself on its regional assortment of crayfish, oysters, and much more (Fishbone on Beach Street). Suffice it to say, despite your usual tourist prices, you'll not go hungry in Queenstown.
More than anything, you'll probably be grabbing a drink somewhere in Queenstown, if only because there seems to be an establishment everywhere you turn. The city quickly realized that all of these folks that enjoyed luges, jet boats, mountains, and all that adventurey jazz also really liked to stay up until four in the morning with their friends. Again, if you start at the Mall, you'll immediately find a good five places to interest you in the surrounding blocks, from backpacker-oriented, cheap dive bars (Buffalo Club, Winnie's, Cowboys, Altitude), classic pubs (Pub on Wharf, Pog Mahones), and classier bars (Naughty Penguin, Bar Up, Barmuda) that will run you a hefty tab. The good news is that people love to go out and there is always great energy from the mix of locals and travelers.
For more on what might be available in downtown Queenstown, browse our links.