East coast whoot whoot!
My favorite place is Massanutten mountain. Free camping along the trail and very scenic for multi day hikes, and it loops. Very beary so be conscious of that.
West Virginia by harpers ferry has a lot of day hikes some easy some hard. Fun for a day trip but maybe crowded. Maryland heights trail, loudoun heights and the civil war hike is pretty cool too. You could also stay at the Koa in harpers ferry and day hike down to historic harpers ferry. The c&o towpath is there also. C&o has free camping for hikers and bikers from Cumberland md to d.c.
shennadoah national forest has a lot of cool day hikes and if ya feeling froggy do the whole skyline drive 100 miles very strenuous.
- cacapon state forest is another great hiking spot.
- great falls park is on the C&o too, I think certain parts are closed right now for maintenance though
This is just a few, lmk if ya have any questions about more specific location.