My recommendation would be to travel a little ways to Jamestown, take the VA. DOT ferry (free) to Surry. Then drive about a mile to the Surry House which has been reviewed here. The food is great.
In Williamsburg, there’s a good local place across the street from the Cracker Barrel, but I can’t remember the name. It’s frequented by both locals and tourists.
Another place that I like, mainly because I like the chain, (it’s a small chain) for BBQ is Red Hot & Blue. The Q is decent there.