Suggestions with kids
My kids of the same age really enjoyed the miniburgers and pizza at Matchbox for lunch.
It is on China block near the arch. Kids always get a kick out of that.
Closer to where you will be staying, Tonic @ Quigley's Pharmacy should have something to please all ages.
We went to 2 Amys a couple of weeks ago on a Saturday night (I know, crazy busy!) and were told it would be a 45 minute wait. My 6 year-old daughter (who needed to eat immediately) wanted to go to Sushi Sushi across the street. So we did a roll each for an "appetizer", and by the time we were finished, our table was ready at 2 Amys.
The sushi was pretty good, but 2 Amys was amazing. The seasonal appetizers are simply prepared, top quality ingredients. The thin crust Neapolitan pizzas are delicious. I think of it as DC's answer to NY's Otto, only with fewer wine choices.
Best of all, it's a stone's throw from the National Zoo, which is free. Go see the pandas, and the new baby anteater.
And for goodness sake, don't buy your food at the National Zoo! The food offerings in the Zoo itself are dismal. You're in better shape at any of the Smithsonian eateries; the food isn't gourmet, but it is edible.
Foggy Bottom isn't that far from Vidalia, where you'll enjoy an upscale take on Southern cooking. Vidalia isn't cheap, but your kids may fall in love with the bread basket and onion compote--and should be welcome if you choose an early dining hour.