On the dining plan?
At the Beach Club itself, the only options are Beach Club Marketplace (sandwiches and salads - no burgers, no nuggets) and Hurricane Hanna's at the pool (burgers, hot dogs, grilled chicken, grilled cheese)
Beaches & Cream will apparently be temporarily serving CS breakfast (lunch and dinner are TS).
Not at the Beach Club itself but in the same general area: Boardwalk Bakery, and continental breakfast (no meals offered besides breakfast) offered at the Ale & Compass Lounge (Yacht Club) and the Bellevue Lounge (Boardwalk).
That's it on the dining plan.
If you're not on the dining plan you can also take advantage of the kiosks situated along the Boardwalk, the Spoodles Pizza Window (fate of this is not certain since Spoodles closes on August 2 to transition to a new restaurant, Kouzzina) and the Picabo cafeteria at the Dolphin.