The notion of “Eastern Shore” varies among those asked, but one workable definition might be what is also known as “Delmarva”—Delaware-Maryland-Virginia, all of which states have a presence on the peninsula bordering the Chesapeake Bay. That term is often used on the peninsula, too. After all, to what state you belong can be less important than who your neighbor is.
Crossing the Chesapeake Bay Bridge is quite an experience and best conducted via open car. Once you reach Delmarva, you're in a distinctly more rural area than the greater Washington area you just left. It isn’t necessarily the bucolic rural scene one might expect. In many ways, it’s just a huge space for modern franchises and malls—but widely separated, reflecting the small population density. Oh, and chicken farms.
But there’s history, too. Several areas were well developed by the time of the Civil War. I don't know how far back in history the town goes, but the actual destination shown in this web site is officially called Assateague Island National Seashore, a national park. Ed Lohoski led this trip, as he had actually been here before.
I suppose there's really little that distinguishes the park from many others, but culturally there is the presence of wild horses, which are called Chincoteague Ponies. The ponies swim each year to Chincoteague Island, in a fundraising scheme, and this gets decent publicity [see “Horses” in the link to Assateague].