I've been in Washington DC for nearly 40 years now, and I've eaten everywhere.
Ignore all recommendations for chains -- The Palm, Joe's, etc. You can eat at these in a lot of other cities.
Inn at Little Washington is worthy of its 3 Michelin stars, but is a trek out of town and probably comes with an $800/night room at the Inn.
Fiola Mare is the best seafood restaurant in Washington DC right now. Marcel's has the best service of any restaurant in Washington DC. Komi is one of the best restaurants in Washington DC, with Johnny Monis as Washington's best restaurateur.
Washington's best chef is probably Eric Ziebold, who was chef de cuisine at The French Laundry. His Mount Vernon Square restaurants are not to be missed -- Metier and Kinship. But if they are to be missed, miss them for Corduroy, Tom Power's excellent and not-to-be-missed restaurant.
I have not yet been to Pineapple and Pearls, but it is getting national acclaim.
If you have some time, join
www.donrockwell.com and do some research. It is a powerful source of information, and all of Washington's best chef's are on the board most of the time. If you're nice to Don Rockwell. he'll connect you with any of the chefs.