My boyfriend rides his bike on the Schulykill River path, Kelly Drive and in Fairmount Park. We haven't been to Wissahickon Park yet, but a friend goes there often. These are all easily accessible from Center City. A little farther away, there's Valley Forge Historical Park, which is quite pretty, and the Brandywine River Valley on the border of PA/DE is gorgeous. Nothing truly mountainous, but you'd still want a decent bike to go riding around the parks. If you're skittish about riding it to school, just get a junker for that and keep your good bike for when you want to take really nice rides.
Also, the SEPTA trains allow bikes during off-peak hours, so you'd be able to get out of the city for a day to go riding if you wanted to.