For lunch, go to the Cheese Shop. It’s in the colonial area and so good.
For a sort of unsuspecting place - try the Carrot Tree. Again, it’s a lunch (or breakfast) place. We went there on a whim years ago and were blown away by how good it was!
For a good Italian dinner in a relaxing and kid-friendly place, I would recommend Maurizio’s. It’s sort of a typical suburban Italian restaurant, but the food is phenomenal (especially the bread!). We used to have to go to Williamsburg every year for years for dance competitions and ALWAYS ate her.
Another +1 to the taverns. Go for the experience, though, not with the expectation of five-star dining.