Central and North-Central PA should be good that time of year. For Central PA, I would give the Feathered Hook in Coburn (fly-shop and fishing B&B a call. You might even stay there at the B&B if you don't feel like camping (or for the first night to have a place to stay if you leave right after work).
Up further in North Central PA, Pine creek if you really want a remote stream. There are good hikes into the pine-creek gorge. I've fished up in that area but not camped. There are reasonably priced fishing oriented hotels/inn's up there too.
Pine and Kettle creek come to mind, but there's a lot of water there to cover.
Stocked:
Wild:
Don't knock the stocked water. If you focus on C&R or delayed harvest water, the fish are good and plenty over-summer.
Plan for rain that time of year. It's good for fishing, but not as fun for camping.