I-95 beat me to the punch. Gadsby’s is THE place, both atmosphere and food for Thanksgiving.
The other best location is at the Mount Vernon Inn. However, I would suspect that both places are booked and the waitlists are long.
Other places to look at are:
Morrison House Hotel Restaurant (a tad expensive)
Cedar Knoll Inn
If you’re willing to come into DC (metro accessible from Old Town) some reasonably priced (under $50) dinners include:
I’m not sure of the price, but Bistro Bis usually has a Thanksgiving meal, as does its sister restaurat Vidalia. Both are excellent, but I’m bot sure of cost.
Other great independent restaurants you might try (not guaranteed that the menu is traditional thanksgiving, but they may be open) include:
Fish Market Restaurant (an Alexandria classic, great (sea)food and atmosphere)
Bilbo Baggins Restaurant
219 Restaurant-219 King Street, they are definately having a Thanksgiving meal, but$$$price fixe $75)
Union Street Publick House (I really like this place, it’s one of my mainstays when I’m in Alexandria, but I don’t know about its T-day offerings.)