Most convenient place to stay when going to Heinz Field or PNC Park would be on the North Shore. I saw you will be staying in town which is still within easy walking distance to the stadiums Clemente Bridge (6th street bridge I think).
North Shore has plenty of hotels, bars and restaurants within easy walking distance. Additionally, there is a Casino (must be 21 to enter), the Pittsburgh Science Center (with Omnimax theater) children might enjoy ages? and the Andy Warhol Museum. Restaurants (moderately priced) on the North Shore include Bettis Grille 66, Bar Louie, Tequila Cowboy etc. (many have outdoor dining weather permitting)..An upscale restaurant located on the North Shore would be Hyde Park Restaurant.
If you are staying downtown, you can walk to see Point State Park, Fort Pitt Museum and Market Square which have many moderately priced restaurants and higher end ones including Morton's and a Ruth Chris.
Great views of the city can found at the Mt. Washington Restaurants. Two good ones are Lemont Restaurant and Monterey Bay Fish Grotto. Most restaurants on Mt Washington are upscale and pricey.
Pitt and CMU(Oakland area) are about 4 miles from Heinz Field/PNC Park so you would have to take a cab over to see the campuses. Additionally, across the street from the Pitt Campus there is the Carnegie Museum (great dinosaur collection) and Art Museum and Phipps Consevatory.
Located on the South Side (need a cab) the Haufbraus House Restaurant (moderately priced-always Ocktober fest) is fun or Cheesecake Factory.
You can google most of the sites I referenced to decided if you have any interest.
Pittsburgh is a fun city have a great stay.
HAIL TO PITT!!!!