For one price of admission you get access to the Museum of Natural History and the Museum of Art!
Did you expect us not to suggest going to the zoo?
A great botanical garden right next to Schenley Park
Take in the views of the city from Mt. Washington and then ride the incline down to Station Square!
The South Side is a park of town known for it's nightlife. It has a variety of bars, restaurants, and other attractions. We recommend the Tiki Lounge for a unique, kitschy (in a good way) atmosphere and the Urban Tap for their brunch.
If you want to do some exploring, check out the Strip District and Butler Street in Lawrenceville. There are plenty of small business and historical spots to find.