I would head to Eastern Market...there are a bunch of options in that area. I like Matchbox and Cava. I also hear good things about Ted's Bulletin.
Also a little closer to the Capitol there is Good Stuff Eatery for delicious burgers and shakes (I personally prefer the turkey burger).
Good Stuff Eatery
303 Pennsylvania Ave SE, Washington, DC
505 8th St SE, Washington, DC 20003
Well I don't have kids but my brothers and sisters do so I would suggest-
Tortilla Coast, Tex Mex, a Cap Hill standard place and kids love Mexican
We The Pizza, kids love pizza
Matchbox, kids love pizza again
Johnny's Half Shell, seafood, more upscale than the others
Tortilla Coast and Matchbox highly recommended
Johnny's Half Shell
400 North Capitol Street NW, Washington, DC 20001
400 1st St SE, Washington, DC 20003