There is a continental breakfast menu available inside the Boardwalk, on the Inn side, in the Bellevue Lounge. Lots of places to sit too, both in the lounge, in the lobby, or out on the verandah overlooking the boardwalk.
ETA: If you are on staying in the Villas, even a studio has a fridge/freezer, toaster, coffee-maker, and microwave. You can buy breakfast materials in the Screen Door. We always buy bagles and cheese.