H St. has the majority of restaurants, pubs, bars, and cafes in the neighborhood and is only a 10-15 minute walk down 14th or 15th St. You can get anything from pizza and beers to Ethiopian or Thai food--and everything in-between. This map will show you the walking route.
Washington.org's Review of H St. Cuisine--also broken down into specific DC neighborhoods.
Also a quick 15 minute walk from the apartment with good coffee, restaurants, and pubs. There's also a nice community market and street fair every weekend. Be sure to walk through Lincoln Park on your way--created not long after Lincoln's death and inaugurated by Frederick Doughlas in 1876.
Foursquare list of breakfast/brunch spots in the neighborhood.
Union Market is 1.5 miles from the apartment and is a recently renovated inner-city market that includes restaurants, bars, shops, a food market, and even an independent movie theater. Here's a link to the Union Market website: