For a beer nerd visiting Pittsburgh, here's what I'd recommend:
-Visit East End Brewing in East Liberty if you can.
-The major brewers are great if you can hit them, though they're the obvious, big blips on the radar: Penn, Church, and Hofbrauhaus
-The next type are the popular 'beer bars', many with multiple locations: Sharpe Edge, Bocktown, Full Pint, Rivertowne, Rock Bottom...
-Then there's the bars that happen to have a great selection: Fatheads, The Library...Nola in Market Square is pretty good...and various bars in the southside will surprise you here and there with something like a Rogue Dead Guy, DFH, or something of that caliber.
-Finally there's the gems, little places that are all about the beer. The biggest example I can think of right in Pittsburgh is D's 6-packs and Dogz, in Regent Square. They have a second shop in Monroeville that, while good, isn't AS good as the Regent Square location. No nonsense 'beer bar' with both a respectable tap listing, as well as their 'beer cave', which contains 5-600+ beers, easily, including plenty of hard to find beers. It's not necessarily big on atmosphere in the strictest sense, but in my experience, beer nerds kind of like the no-frills, 'all about the beer' attitude.
If you're able to stray from the city proper, three places within an hour that are definitely worth the trip:
Mister Bones, in Greensburg. A tiny sandwich shop with a small but impressive selection, including some often hard-to-find stuff. It's not really a place a visitor will want to spend all day there...but it's got good food at good prices, with a few craft brews to wash it all down. Small outdoor patio if it's nice. Among many others, off the top of my head, you can find stuff here from Lagunitas, Great Divide, Victory, Rogue, Stone, Sam Adams, Sixpoint, Ithaca, Oskar Blues. This is the place if you're just looking for a bowl of soup and a sandwich, nothing fancy. Also kid friendly, including a small selection of what I guess you could call "craft pop". Staff is great on general service, but only a few are beer nerds, so if you get one of them, great, if not, you'll likely know it quick.
The Headkeeper, a slightly more upscale tapas bar with a small but well-chosen tap selection and over 600 bottles, about half import and half micro, also in Greensburg. The menu here is somewhat more expensive, but also very high-quality, more interesting, and prepared right in front of you. Where Mr. Bones will have a chicken sandwich, at the Headkeeper, you can get sesame crusted seared Ahi Tuna steak w/ wakimi seaweed salad. While I've seen kids here, it's really not the place for them, as things are definitely focused on these more adventurous tapas dishes and the beer. Also has an outdoor patio with plenty of seating. Same deal with the staff, though the staff itself is much larger. Generally, one of the guys behind the bar will know what's up.
Finally, in New Kensington, there's the House of 1000 beers. There isn't much else to do in New Ken, so it's a trip just for the beer, but the House of 1000 Beers lives up to its name, all in a "garage bar" style setting (concrete floors, unfinished wood & concrete, etc), it's definitely a no-nonsense approach to good beer, with 40-60 good beers on tap, and at least 600 different bottles (and really, it wouldn't surprise me if there were the full 1,000 beers, if not more, on their shelves). Food is the bare minimum. Basically, they'll pop some frozen chicken or poppers in the oven for you, or make you a plate of nachos. Here, from the few times I've been there, all of the staff at least has a decent knowledge of beer, with the bartenders usually knowing their tap selection very well, in addition to their own favored styles (the first time I went, my bartender mentioned that she was a big fan of stouts, another time, the young lady behind the bar was a hop head, etc.).