I was in Pittsburgh last month for 2-3 days, and took Amtrak to & from. I highly recommend:
*going up one incline, walking along the street at the top of the cliff, and coming down the other incline. We went up the Monongahela Incline next to Station Square (bunch of restaurants, shops, and a hotel on the site of the old P&LE RR station) and came down the Duquesne Incline. The sweeping view of downtown and much of the city is spectacular, but the neighborhood up there is nice to see too.
*the river cruise. It's not long (about an hour), and it doesn't go very far, but considering how many of the sights of the city can be seen from the river, it's a great introduction to the city.
*the Cathedral of Learning and the surrounding university campuses (U. Pittsburgh, Carnegie-Mellon) and neighborhood. Of course, go to the top(ish) of the Cathedral for the views. If you have it to spare, allow over an hour to see the Nationality Rooms at the Cathedral: classrooms on the first and third floors lavishly decorated to be reminiscent of the various nationalities of Pittsburgh. And pay the fee for the first floor rooms, don't coat-tail on paying customers.
Also went to a game at PNC Park. Nice ballpark with a very nice view of downtown, but I had nobody to root for and the weather was a bit unpleasant in the nosebleed seats on the wintery "spring" day I attended. That said, PNC Park seats are much cheaper than Wrigley Field seats. Definitely take the free T light-rail subway to/from if you go, unless your hotel is close.
By the way, I think I ran into former Sen. Santorum on the elevator to the top of the Cathedral. I'm not sure if I was him I would wear a jacket with my name stitched on the front at a university campus. (Yes, I know he's an alum.)