Hello! You can check with Recreation.Gov for federal campgrounds and Reserveamerica.com for state campgrounds. These sites will only list campgrounds that accept reservations, though, so you might also want to check with the West Virgina State Parks (
http://www.wvstateparks.com/lodging/camping.htm) for first-come, first-served campgrounds. I cannot speak for the conditions on the east coast, but I know out here the first-come, first-served campgrounds are wide open if you arrive before Friday afternoon.
Can you just pitch a tent anywhere you want? I'll leave that question to someone more local to the area, but you can generally camp anywhere on federal land (USFS or BLM), provided you are several hundred feet from any water source (a general rule, sometimes it is 100 feet).
Good luck!