Definitely an incline trip. There's 2. One in Station Square along with lots of shops/restaurants. And another a little upriver (it's the red one they show in pictures) and offers a little better views of the city.
Point State Park, where the fountains at. Recently reopened.
The strip district (no not that type of "strip"). It's an open air market style area mainly busiest on weekends. Located along the Allegheny river side of the city. Home of original Primanti's and Pamela's (not as famous but definitely give it a Google).
South side (Carson Street) for night life.
Kennywood, amusement park not far from the city at all. Very unique, lots of modern rides with nostalgia thrown in. Was featured in the movie "Adventureland"
Rivers casino and the science center with the WWII USS Requin moored alongside are both on the north shore where the stadiums are located.
Pitt University's Cathedral of learning. Easy to find, huge gothic style skyscraper in the Oakland area where all the universities are located.
Food wise, I love Eat 'N Park but many many more locally owned places (so different than franchised NOVA). If you can, tryn hit up a bakery, Bethel Bakery in Bethel park would be my fav.
I'll be the first to admit, make sure you update googlemaps/WAZE/or whatever GPS mapping you use. There's no beltway up there (the colored belt signs are worthless)
Hope you have a great trip!