I've only been to DC twice myself, and am going back this July for the Man United-Barcelona game.
The new Smithsonian African American Museum is impressive, although I only went to the Music and Musicians part of it, which occupies the whole top floor. Not just jazz, but a lot of one of a kind interesting memorabilia and personal effects from other genres. Chuck Berry's cherry red convertible Caddy is on full display. You must go to their website early in the morning, to reserve admission, otherwise they may not let you in.
National Art Gallery is far out. They run free docent tours several times a day.
The open top bus tours can be fun also, especially if the weather is sunny. Just pick a reputable operator, some of then suck.
The record store scene is understandably much more humble than NYC, and not essential, unless you're on a mission.
Just checked. Roy Hargrove is at the Blues Alley this weekend.