This Smithsonian museum has good rotating exhibitions on the experience of diverse and underserved communities 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, since it often closes between installations.
You'll likely have the place to yourself, as this is the Smithsonian's least-visited museum. It's not the easiest to reach by public transport. 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. A car (there's free parking) or rideshare works best to get here.