The L’Enfant plan of Washington D.C. contained locations for a number of markets, including one east of the Capitol. It was not, however, located where Eastern Market was, but instead where most people lived back then – and where it was easy to reach from the river. Eastern Branch Market is important historically to Capitol Hill, but it is completely eradicated today.
Fortunately, when the Marines expanded their barracks south of the freeway, they first did an archeological investigation of the site, discovering some remains of the old building. Unfortunately, the results of this are no longer available online. A previously downloaded copy indicates exactly where the market was: Between 6th, 7th, L Streets and Virginia Avenue.
Today, the site is taken up by the Marine Barracks annex – currently under construction. Stop by some time and remember how this space used to feed Capitol Hill.