I think you're looking for something that may be a bit hard to find.
Most bars that take cocktails seriously, where you'd find appropriate stemware and atmosphere, don't pay much attention to vodka. It lends no flavor to a beverage. It exists to get you drunk without tasting the booze. Most places that serve a ton of vodka in a fancy glass cater to folks with more money than sense, so they tend to be overpriced (any of the good steakhouses will serve you an excellent vodka "martini", I am sure...and charge you ~$15 or more).
You'll find no shortage of bars in Chicago that serve a lot of vodka, but most of them will not treat it particularly well. Likewise, you'll find no shortage of bars in Chicago where you can get an impeccably made cocktail, but you'll find most of them will not involve vodka.
Cheap is in the eye of the beholder, and varies greatly by your location. Fancy stemware generally isn't found in places I'd consider cheap, though.What price point were you looking for?