There really are no counter service restaurants at the Boardwalk. The availability of CS food is also very limited if you are on the dining plan.
The only approximations of CS restaurants in the Boardwalk area are the Boardwalk Bakery (no inside seating) and the Beach Club Marketplace (very little inside seating) which aren't anything like food courts - their menus are pretty limited and no "kid food" like burgers, chicken nuggets or pizza is available. If what you want to do is use a dining plan CS credit, probably the best you can get is Hurricane Hanna's, located at the Yacht/Beach pool (you don't have to enter the pool perimeter to go there). They have hamburgers, hot dogs and grilled cheese, and kids' meals are apparently served in a plastic pail.
If you're not on the dining plan, there are kiosks along the Boardwalk where you can buy hot dogs, there's the Boardwalk pizza window, and there is also the Fountain at the Dolphin (not really a CS, more like Beaches & Cream) and Picabu, also at the Dolphin (a cafeteria setup with a big selection).