There are also some food carts with fries, hot dogs, chicken, etc... right on the BW. You can always order food to go from any of the restaurants. We have done this many times. Or, walk over to B&C at the BC, great burgers there.
We love the Boardwalk pizza take out window. Also has calzones and salads. The hot dog kiosk is across the walk from there. Has very big hot dogs for a decent price. Also has an assortment of fries. No burgers that I can think of but you can go over to the Beach Club and Hurricane Hannah's poolside and get a burger.