Lots of good advice here, I'll just add a few places I havn't sen mentioned yet that I've enojyed in the past. These are all in Georgetown, I generally don't get up the energy to explore for restaurants elsewhere.
The Tombs is my favorite restaurant to go to - it might be a bit strange if you're not a Gtown student (its right by the campus, at 36th and prospect), but its a relaxed atmosphere, and the food is tasty. Solid burger for 7 or 8 bucks. Brunch is great there too.
If you're up for an expensive night out, 1789 is right upstairs of tombs, and its good (but again, expensive).
My favorite pizza place is Pizzaria Paradiso, on M street (around 33rd street I think). There's also a location in Dupont, but I've never been to that one. They also are supposed to have a great selection of beers in the new basement section, but I havn't tried that out yet.
Quick Pita is another hole in the wall type place, across the street from Dean and Deluca on M street. Its middle eastern type food - I don't know much about that style of food, but it tastes good to me and its cheap also.
Speaking of dean and Deluca, their sushi is cheap, and is a nice picnic type lunch meal for a reasonable price. On a nice day, I like to pick up some of it, and head down to the old aquaduct remains that overlook the Potomac (off the C&O canal, right by the bridge) - a nice lunch date.
I also really like the block on Prospect street that has Bankok Bistro, Peacock Cafe, Cafe Milano, Neyla, and Mortons - all are great restaurants - if I am not sure where I want to go for dinner, I usually wander over there and go to whichever strikes my fancy - never been let down.
Mein Yu is a bit of a funky place on M street - its an Asian/american fusion type place. I ate there once and loved it, though it is both a bit pricy and the atmosphere is...different. Worth a shot, you'll probably love it or hate it.