This Smithsonian museum has good rotating exhibitions on the African American experience in the USA. They typically focus on art (quilts of a certain region; landscape paintings by an overlooked artist) or history (the first black baseball teams in the area; a slave family's story). The museum also serves as a community hall for the surrounding neighborhood of Anacostia. Call ahead, as it often closes between installations.
It's easiest to get here by car or taxi. From the Metro station, take the ‘Local’ exit to Howard Rd and transfer to the W2 or W3 bus. The W2 runs during rush hours, the W3 every 30 minutes.