Palmetto Avenue runs along Edisto Beach, the popular place to see and be seen in this tiny island community. However, to escape from possible crowds, try the lesser-trafficed beach on the bay.
There, you can watch dolphins leap past you throughout the day, while collecting shells not found on the main beach. It's more of a family environment, and more private, with only locals usually enjoying some sun in the early Spring.
To get to the best access route, take Palmetto down and around the big bend, almsot to where the shrimping boats are docked on the back bay. There are a few public access paths that lead to this smaller beach, with room for parking on the grass.
There are a few shore snack for the adventuresome kind. The "Bull Thistle can be eaten if you remove the spines from the stastems. Cut open. Eat raw or add to salads like celery.