Real quick
Places to eat and drink lots of good beer on tap
Fatheads - South Side (A must stop for everyone, although recommend going during the day)
Smokin Joes - South Side
The Library - South Side
Carson St. Deli - South Side
Basically there is a ton of good places to eat and drink on the South Side, but its a mad house at night, especially on the weekend. Dont expect to walk in Fatheads on a Saturday night and be able to sit anywhere.
Industry Public House - Lawrenceville (Beer, bacon, and hipsters)
Mad Mex (several) - There's one in just about every area of town.
Harris Grill - Shadyside
Kelly's Bar - East Liberty
Sharp Edge (several) - One of the original destinations, but pricey and Belgian-focused.
Places to buy beer:
Beer isn't generally available in grocery stores, with some exceptions. It's also not available by the bottle or six packs in liquor stores. You gotta buy by the case from a distributor or by the bottle from a restaurant or six pack shop (which usually sells some hot dogs to qualify as a restaurant).
D's Six Packs and Dogs - Regent Square (East End) and Monroeville
House of 1000 Beers - They bring in a lot of grey market ****, so you're best bet at finding out of market stuff, but seriously marked up. Its also way out in New Kensington, so not particularly convenient if you're not already out that way.
Several of the higher end Giant Eagle grocery stores sell beer. Whole Food in Wexford sells beer, but the Shadyside Whole Foods does not.