Bethesda Crab House is a good experience. Yes, MD crabs aren't in season, but at this time of year they have them flown in from the Gulf (of Mexico) region. Just call a day before to tell them how many dozen you'd like. It's not cheap, but it's an experience.
Oysters are indeed in season. Various restaurants will have them. There's a place on 14th street in DC, a few blocks south of U, that specializes in them. I'm clearly getting old as I can't remember the place now, but I think it even has "Oyster" in its name. In the summer, we've taken visitors to the Eastern Shore (St Michaels) and they have some restaurants there with local seafood, but I'm not sure the hours these places keep in winter -- check ahead.
Chaps is a bbq place in Baltimore. It's sort of unique and down-home, though not seafood:
http://www.chapspitbeef.com/