Just to the south in Eastern Virginia are Chincoteague and Tangier Islands. The former is known for its beauty and wild ponies similar to Assateague, but with houses and rental possibilities, and the latter is the twin of Smith Island, with the same time-stopped-in-the-eighteenth-century culture.
Just north of Ocean City are the perhaps even more popular beaches of Delaware at Rehoboth and Bethany
If looking for more Chesapeake culture, look to the west in Annapolis, or to the southwest in the small historic towns of Southern Maryland. The latter is a bit hard to reach by car, but a very manageable boat ride. Or even look north to a very different culture, but one still firmly tied to the Bay, in the big port city of Baltimore.