Assateague State Park in Maryland (close to Ocean City) would be my choice. It's just over the dunes from the beach, but it only has one loop with electric so you need to make reservations a year in advance for peak times, or get lucky, if that matters. If you can do without an electric hook-up (generators are allowed except for quiet hours) there are lots of non-electric sites at the State Park. The nearby National Park also has no hook-up sites, but only cold water showers.
First Landing State Park in Virginia Beach, VA is also just over the dunes, but a bit longer walk over limited boardwalks. It is barely inside the Chesapeake Bay, but has a wide beach and some waves, and it's an easy drive to the Atlantic Ocean beaches if that is a priority.