Like GalleyWench, I usually park at Ramada Park N Jet. I always call ahead to make sure there are spaces available. Otherwise, like rittenhousesq, I'll hop on SEPTA from Center City.

Edit: The Philadelphia Parking Authority (state run) controls parking at a city owned airport. I don't trust them at all. They towed a friend of mine's Subaru (AWD vehicle) without using a flatbed tow truck (this occurred in Center City), and damaged the rear differential. Not only that, he was not illegally parked as they claim.