Phipps conservatory is really cool if you and/or like plants/flowers. Its in Schenley Park, easy to park and (free or a couple bucks), Oakland is a 5 min walk and you can see Pitt/Carnegie Mellon/Oakland.
National Avairy has a nice bird collection.
Touristy areas: Carson st (bars, sometimes difficult to park). A little down the road from carson st. is the Gateway clipper which you can take to the game.
Strip District - which has good delis, decent food, and is the worlds capital for unlicenced steelers stuf.
Some Carnegie museums that I haven't been at for a long time so can't comment on. There is an andy warhol museum as well I haven't been too.
Photo places: West End, Mt. Washington (take the Duquesne incline to get there).
Food: City does sandwiches and bread/bread for sandwiches + italian pastries as good as anyone in the country. The Primanti's in the strip is good (any other Primanti's is a seperate chain; the UNO of sandwich shops). Many of the best places for sandwiches are places what looks to be in the middle of nowhere like Big Jims, Triangle Bar or (south of city) DiCarlos Fruit Market.
All the parks in the county are nice: Schenley, Frick, Boyce, South Park (10 mi south of city) is huge.
Generally you can just go downtown walk and explore. Its just a nice city and the hills gives the neighborhood a uniqueness and character.