On any other day I'd have all kinds of thoughts, but this year MLK day falls on the day before the Inauguration, and DC is going to be absolutely mobbed with visitors. All the hotels are sold out, Metro will be packed as I imagine all the tourist sites will be too, even though you're not looking for the "mainstream" stuff I imagine just getting around town would be a challenge,

How about Annapolis? You could easily get there in an hour or so, have a nice lunch somewhere, explore the town, maybe a visit to the Naval Academy...easily be home by 4:00.