If you will be by the Convention Center during the day and can afford a lunchtime escapade, Proof (7th and G NW) is one of my all-time favorite restaurants. They have a lunch special at the bar which includes a choice of main course as well as a drink (soda, iced tea or glass of wine) for $12.
They're deffinitely worth a try for dinner as well, though it likely wouldn't be a 'budget choice'.
For a nice sweet treat, try Pitango Gelato on P between 13th and 14th NW, which is right near where you'll be staying.