Terrapin Nature Park is located just north of the Chesapeake Bay Bridge. To get to the park from most of the state, you will need to cross the bay bridge (with toll) and turn off in Stevenson, MD. Terrapin Nature Park is a nice alternative to Sandy Point State Park, with picnic areas and a public beach. There is also a nice 2.5-mile loop through the park amidst marshes/wetlands and meadows.
There is no entry fee to the park. For more information, check out the Terrapin Nature Park website.