Bunch of good museums downtown. Do NOT expect to drive downtown on a weekend. On my one and only visit we stayed in a suburb, and when we went to drive downtown they closed the one and only freeway.
Downtown on a weekend is easy. It is true, there is one and only one freeway in from pretty much every direction, but lots of alternate routes on which locals should be able to advise if necessary.
In addition to the previously mentioned Heinz History Center (well done, but mostly Pittsburgh-centric) and the Frick House, I would also recommend Phipps Conservatory, which is in Pittsburgh's Schenley Park, near Univ. of Pittsburgh and Carnegie Mellon Univ. I'm not much of a plant and flower person myself, but the displays are so well done that it's an enjoyable walk-through even if floral isn't your thing.
There are a number of good restaurants in and around the city, and everyone's tastes are different, so it's hard to advise one way or another.
This one is decent and family-friendly:
http://www.churchbrew.com
Excellent seafood (for Pittsburgh, anyway) lunch place:
http://www.pennavefishcompany.com
Even though I'm a native of Pittsburgh, I consider Primanti's to be a complete dive. Most out of town guests seem to have no idea why Pittsburghers rave about it and, quite frankly, neither do I. French fries and cole slaw on a sandwich may seem clever, but it's not my thing.
JKG