Archibald's sandwiches are pretty good ;-) lol
Lauriol Plaza is a favorite...a few blocks north of Dupont Circle.
http://www.lauriolplaza.com/
I've never done this with a date, but I think it would be cool to go down to the waterfront and get some spiced peel and eat shrimp and go to East Potomac Park and watch the planes take off :-)
If you're looking for something of a "local flavor"...go to any "carryout" in town and order Chicken Wings & Mumbo Sauce. Mumbo sauce is decidedly DC. It's something of a cross between a sweet and sour sauce and a bbq sauce. Try it!
AND...for crabcakes...sorry DC, you'll have to make the trip into MD. Avoid Legal Seafood, mayo isn't supposed to be in a crab cake :-( Go to Jerry's Seafood in Landover Hills
http://jerrysseafood.com/main.php
or, head on up 295 to Dorsey Road to Timbuktu
http://timbukturestaurant.com/ What the lack in ambiance, well, the crab cake more than makes up for it.
Happy eating!