Hi Casey,
When I used to live in Center City, I would go to B&A Archery in North Philadelphia. The owner is a nice guy and there are occasional trad shooters there. It does get crowded at night though so try to go during the day.
Also, check out Wapiti Archers of Pennsylvania in Fort Washington. They host open shoots on the First and Fifth Sunday of the month and they have a good group of trad shooters who helped me out when I was first starting.
If you ever make it out to West Chester, KodaBow has an indoor archery range and I think they give lessons. And, you're more than welcome to come fling a few arrows with me. PM me if you have any questions.
Cheers,
Evan