Howdy, unfortunately there is no sandy beach although the "beach" sites do backup to the water. It is just a few minutes to the Port A ferry and plenty of beach, we seldom miss spending at least a day on the beach when we visit GI. The park does have a very nice lighted fishing pier and free wifi.
Our favorite places to eat in Fulton/Rockport are
Pop's a small bar/restaurant/dive on the same road as the park
Alice Fay's on the Bay road in Fulton, good food/dive bar (cheap breakfast)
Charlotte Plummer's for better dining experience, DW loves the taco soup
Boiling Pot when a little seafood isn't enough