There is on-street parking, but it's metered, and either a 2-hour or 3-hour limit. The Parking Authority is pretty aggressive about enforcing the meter rules, so I'd avoid the meters.
My recommendation for parking is the lot at the University of Pennsylvania Museum of Archaeology and Anthropology. It's very convenient for those exiting I-76 at South Street, as it's about a block from the exit, at the corner of South Street & Convention Avenue (it would be to your left, after driving on South Street for a block, after getting off I-76). (For those using a GPS, set it to 3220 South Street, Philadelphia, PA.) Basically, you turn onto Convention Avenue, and then at the end of the parking garage you turn right into what appears to be a small alley to actually enter the parking garage. (Signs are somewhat lacking for this.) This is the closest lot to the Palestra. The only downside would be if you're going to the Tap Room, in that it's a bit of a walk from the garage to that (you'd pass by The Palestra).
There's also a lot near 31st Street & Walnut Street. I forget the specifics of how you enter that (see the map that someone linked in the thread).
If the Museum lot is full, you could continue on South Street until 34th Street, then turn left, and then park in the Hospital of the University of Pennsylvania parking garage (it will be on the left side of the street, after you turn onto 34th Street).