How much can you travel? Comet ping-pong has very good pizza, plus the kids get to play ping-pong all night. It's north of Van Ness, so not downtown at all, but I think they'd really enjoy it.
One lunch should be at Mitsitam, in the American Indian Museum.
Another good dinner would be at Matchbox (the main one is in Chinatown; a new one opened on the Hill, but I haven't been). Get a big platter of mini-burgers, which come with the best onion strings ever, and the kids will be thrilled.
How adventurous are they? Ethiopian, which is eaten with your hands, could really amuse kids. No utensils to deal with? Every kid's dream.
Oyamel might be fun, too. They have a great array of tacos that can be ordered individually, so the kids could be creative.
I recommend Founding Farmers (close to Georgetown)
Comfort food-trendy vide-new place, casual.
I went there this past weekend-everything we ordered was good:
THE BEST grilled cheese sandwich & tomato soup, pot roast & mashed potatoes, lobster mac & cheese. Appetizers were salad, fried green tomatoes, bacon lollipops.
INSANE carrot cake for dessert. Many other interesting things on menu.
These are all great recommendations.
I would also add Filomena if they like big plates of pasta and slices of cake. The servings are large so I imagine 2 of the kids could share a dish.
If they like seafood you can try Hank's Oyster Bar. Just a fair warning though, the restaurant is really small, so if they are the type that likes to move around a lot this might not be the best place.
For low-key, cheap eats I like The Diner and Open City. Cal Tort is also good (a local fast-food style restaurant).
For higher-end I've seen children at Central and have also heard that they treat kids well at Brasserie Beck (but I've never seen kids there personally).
Most kids love Two Amys (pizza) in Cleveland Park. In the same neighborhood, there's also Cafe Deluxe. Open City (in Woodley Park) would be good too. Clyde's (my favorite location is in Friendship Heights; they have a toy train that runs on a track on the ceiling, but they also have other locations in Gallery Place and Georgetown).
The previous poster mentioned Filomena, but in my experience that's a really adult-oriented restaurant.