I'm not sure when you'll be in town, but I do full moon photowalks on the Mall. If you are spending most of your days in DC, I would highly recommend eating along the Metro center corridor. There are probably 30 restaurants around the confluence of E/Fst and 12/13th st. Also 7th street has a ton of restaurants, they are a little more touristy though. Chinatown is right there and my absolute favorite place to eat is Eat First on 6th and H. Matchbox, which is a pizza place is on the same side as Eat First.
If you'll be in Alexandria, there are some nice places to eat down by the waterfront and also over in the Del Ray section of the city. If you have time to go to Luray, make sure to stop at Thornton River Grill in downtown Sperryville which is the intersection of 211 and 522. They do close between 2pm and 5 I believe.