A few notes from a Virginian:
(1)
Pierce's BBQ (follow the signs from the "Lightfoot, Virginia" exit off og I-64) is definitely a family-friendly stop to make. Specializes in NC-style BBQ using the Boston butt cut only. Lots of outdoor tables and they just, also, started serving breakfast.
(2)
The College Delly across from William & Mary (as was previously recommended) is also a good, sandwich stop also with outdoor seating.
(3)God forbid that any type of even regional chain should be recommeneded on this forum

but Williamsburg also has one of the Virginia-based
Red, Hot & Blue restaurants (also kid friendly) with great BBQ plus more selections. (This is the joint where Lee Atwater -- advisor to the first President George Bush -- was an early backer.)
(4)Lastly, if you're travelling to Williamsburg from I-95 and coming from the north, a great place to eat just one-mile off of the Interstate -- and a place that has somehow escaped the Sterns' books -- is
The Smokey Pig off of the Ashland, Virginia exit located about 15 miles before reaching Richmond (west off of exit then south on Rt. 1, restaurant will be on your right) which always has cross-section of customers ranging from blue collar diners to nearby Randolph Macon College professors and has consistently been voted the best BBQ in Richmond.
Enjoy and thanks for the spent tourist dollars!