I dine by myself all the time. In DC I frequent Bistro du Coin, Heritage India and Hank's Oyster Bar. But a short metro ride will take you to some excellent recommendations including PS7, Central, and Zola....all have excellent bar dining scenes and top-notch food.
777 I Street, NW, Washington, DC 20001
Hank's Oyster Bar
1026 King St Ste 1, Alexandria, VA 22314
2400 Wisconsin Ave NW Ste A, Washington, DC 20007