At happy hour, Orson
(508 4th near Bryant) offers "classic cocktails" (i.e. well drinks) for $5, your choice of a martini, Manhattan, margarita, or southside (a Chicago specialty made from gin, lemon juice, mint, and simple syrup). These drinks are good, but note that the regular specialty cocktails, such as the "black Manhattan" made from top-shelf rye and Averna, still cost $9, and are arguably worth the higher price.
There aren't any discounts on the food, either, but the duck fat fries ($7) are definitely a good value. These are a perfected, grownup version of the McDonald's style, thin and crisp with a creamy center, and the browned-butter béarnaise dip served with them is amazing stuff. Orson's happy hour runs from 5:00 to 7:00 p.m., Tuesday through Saturday.