Agallagher is right in that there are not a lot of full service restaurants of note in your immediate vicinity. However, there are several pretty good and interesting lunch places in the Mall area, and a number of very good restaurants within a five-ten minute subway ride.
Of all of the eateries that I have tried at the museums along the Mall, the most interesting is the Mitsitam Cafe at the National Museum of the American Indian at 4th and Independence Avenue SW. There are five food stations there, each with a different menu of dishes from a different region of the Americas focusing on indigenous Native American ingredients.
A very different, and more traditional food court is the one found on the lower level of the Ronald Reagan Building & International Trade Center at 1300 Pennsylvania Ave. NW. You can get everything from Chinese food to ribs, seafood and sandwiches and sweets here, and some of the vendors will give you free samples.
Another very good lunch place that is within walking distance of the Mall is 3rd and Eats, a sandwich place at 500 C St., NW. It’s a small, non-profit restaurant run in partnership with Community Family Life Services for the poor and homeless, and it not only competes with the big boys, it thrives by serving abundant portions of meats for made-to-order sandwiches.
For lunch or dinner, the afore-mentioned Johnny’s Half Shell is great. It’s about a 5-10 minute walk from the Capital building, or a 20 minute walk from your hotel. Their fried oyster po’ boy is excellent, as is their key lime pie. http://www.washingtonian.com/restaurantreviews/1009.html
If you’re willing to ride a couple of stops on the subway, there are, as agallagher suggests, a number of good places to eat near the Gallery Place-Chinatown-Verizon Center stop. The previously mentioned Full Kee is in this area (delicious meal-in-a-bowl soups), as are Matchbox (great mini-burgers and pizzas) http://www.matchboxdc.com , and Jaleo http://www.jaleo.com .