We walked to the Eastern Market on a Sunday AM when there is also a flea market in the streets surrounding it. We enjoyed our visit and bought some olive oil and are considering purchasing a painting we saw. If we had driven to DC, we would have bought more.
The Eastern Market itself is a public hall. It's long and narrow and has food stalls along each side and you stroll the center. They sell meat, cheese, vegetables, baked goods, flowers and all of the traditional street market goods. It's not as big or extensive as similar European Markets, but if I lived in the neighborhood, I'd skip the grocery store and shop here.
Outside there were vendors selling soap, olive oil, art, old furniture, new handmade furniture, clothing, and some food carts.
The Market is about 20 minute walk from the Capitol. There is Metro Station there.
If you are visiting DC and looking for something that isn't politics or history, give the Eastern Market Flea Market a try.