Washington DC is 40 miles south and a 45-minute Amtrak ride, with its own massive offering of free museums and memorials. Annapolis, the state capital, is 30 miles east — a beautifully preserved colonial-era sailing town on the Chesapeake Bay, with the Naval Academy and excellent seafood. Both make excellent day trips on Amtrak or by car.
The Chesapeake Bay is the main geographic fact of Maryland, and spending a day on the water — on a boat out of Annapolis, or at a waterfront town like St. Michaels on the Eastern Shore — is one of the best ways to understand what makes this part of the country distinctive. St. Michaels is about an hour's drive, and the Eastern Shore's combination of flat farmland, watermen's villages, and the best blue crab on the bay justifies the trip.