Most everything you would want most to see and do is accessible by Metro, 2 closest stops [walkable from much of Adams Morgan] are Dupont Circle and Woodley Park – Zoo. Adams Morgan night life is lively and nearby U Street nightlife also.
I agree with @dpworkin Holocaust museum is impressive. And the architecture is as compelling and evocative as the exhibits. And it is right next to all the Smithsonian museums.
The Smithsonian’s Freer Gallery with its spectacular Asian art collection and its splendid collection of works by James Abbott McNeill Whistler including his recreated Peacock Room is really worth seeing and more of an undiscovered treasure than such things as SI’s Air & Space. [Smithsonian Metro stop for Smithsonian mall museums and Holocaust Museum].
The National Portrait Gallery and American Art Museums [one building] have been totally redesigned and include an open conservation lab, where you can watch conservators at work behind glass walls [Gallery Place Metro stop]. Chinatown is just up the street, walk a block north and turn right at the beautiful Chinese Gate and go down to Tony Chen’s—either Mongolian stir fry on lower level or traditional Chinese [with emphasis on seafood!!] on second floor—both are great.
Yes go to the Capitol and visit your congressman and explore the tunnels connecting all the Capitol office buildings [you used to be able to ride on the little train that ran between buildings underground but I think that is off-limits now], mail your letters from one of the Capitol post offices [in different buildings or the touristy one at the Capitol itself] and then go to Hill hangouts Bullfeathers or Tortilla Coast on First Street SE a few blocks away and maybe run into him again [Capitol South Metro]. And the Library of Congress is impressive. Grand building, terrific exhibits, and do go into the main reading room!
And much much more.