Here are two possibilities for dinner after Avenue Q. Both are a shortish streetcar ride away from the theater; both do "American" style food.
Chow is a casual place that is good and moderately priced. We've been there once before with a large group.
Zuni Cafe is quite good and not as moderately priced. I've had appetizers there once; it's been on my "I should try this" list.
Any preferences? Other suggestions? I should probably make reservations.