Mad Mex has the best happy hour in Pittsburgh if you're a beer drinker. The Shadyside location boasts 20+ taps of high quality brews, all of which are half price from 4:30-6:30. While l I find the restaurant's proudly inauthentic Mexican-ish fare rather mediocre (carnitas burrito/enchilada and mahi salad are bright spots), their wings are some of the best in town and also half off during happy hour.
In addition to their excellent happy hour, Mad Mex frequently runs other generous specials and will send you a voucher for a free burrito on your birthday if you sign up for their mailing list. They also send out some nice coupons via snail mail and their e-newsletter, so you can get some great deals if you pay attention.