Many of the restaurants will do a Sunday only brunch.
Smokehouse had an awesome brunch. Skull Creek Boathouse was another I tried last week. Full breakfast buffet, or you can order off the menu. Pretty reasonable.
Regular breakfast places - you must try Palmetto Bay Sunrise Café. Top notch food and continually the best service at any restaurant on the island. 2nd runners up - Plantation Deli or Skillets.