As a generalization, your very high-end restaurants will be open (almost always doing a special Thanksgiving menu), and your very low-end 24/7 restaurants will be open (Dennys, Awful Waffle). The ones in the middle--most casual chains, pizza places, fast food joints--tend to close.
If you have a place in mind, probably best to call a week or so in advance to verify. If you decide to go high-end, might want reservations as well.