In the Grayson Highlands, you can camp anywhere you choose. There are shelters with camping areas adjacent, and there are some fairly obvious places (not near shelters) that get frequent use (the marked water source and worn paths are the giveaways) - but you're not restricted to any of these.

I've also been along the AT in Shenandoah NP, and don't recall any restrictions requiring use of huts or designated campgrounds (at least in the Southern section), but you'd want to check for sure before going there; my information is old, and memory may not be entirely correct.