McConnell's Mill State Park is one nice place to hike near Pittsburgh. It's located 40 miles north of Pittsburgh off of 1-79. They have hiking, rock climbing, beautiful waterfalls, and many scenic overlooks. I'm planning on going back to Pittsburgh in May, and I'm going back to this park again.
A little further away is the Laurel Highlands Hiking Trail. It's about 70 miles southeast of Pittsburgh. It's very scenic and has a wide variety of trails for all activity levels.
Racoon Creek State Park is about 40 miles from Pittsburgh and has both short and long trails, depending on how much time you want to spend there. The wildflower reserve is a very pretty place for a walk.
Here is a link to PA state parks:
http://www.dcnr.state.pa.us/stateparks