Great choice staying at Cambria Suites. Right next to the CEC. Place is usually jumping before and after a game (especially a win).
Inclines/Mt. Washington
Carnegie Mellon University (it's computer geek heaven and the building designs are unique)
Carnegie Museum of Natural History
Andy Warhol Museum
Roberto Clemente Museum
Phipps Conservatory
Cathedral of Learning
Parks: Schenley, Point State, Frick Park
Rivers Casino (if you like that kind of thing and you don't mind smoke).
Clubs: Stage AE down by Heinz field. Lots of restaurants in that area as well. Not sure about other night life hot spots though.
Food: Primanti's, Church Brew Works (old church converted into a restaurant)
Skiing: Not sure if any of these will be open - Boyce park, Seven Springs is my favorite but it's not close.
Lots of old theaters as well.
Enjoy!
We rented a car and were able to park right at Cambria which was a real bonus.