In my seminary days, I traveled through that region a few times. Not sure how far you want to drive, but Catoctin Mountain Park near the PA border has trout. Here's a link to the fishing page of the National Park Service sight:
Also, Shenandoah National Park in VA has trout and Antietam National Battlefield in Sharpsburg, MD lists brookies, browns, and rainbows as species in Antietam Creek. They do let you fish in the creek, but close certain parts of the stream to protect the historically valuable. I can't vouch for the quality of the trout fishing, but a few phone calls should get you the information you need. Here's the link to Antietam:
I never had the opportunity to fish these places, but they are worth a visit simply to sight-see.