Kid Friendly Restaurant near the Smithsonian / Mall
I would also add Nando's Peri Peri (the Peri sauce is spicy, but the plain or garlic sauce is good for kids, of course my niece liked the spicy go firgure). Ella's Woodfired Pizza (other things besides Pizza). They also liked California Tortilla and Tortilla Coast as those were easy for them to navigate what they liked on the menu.
400 1st St SE, Washington, DC 20003
Good Stuff Eatery is counter service burgers, fries, and shakes. The toasted marshmallow milkshake is Food of the Gods. I also dig the mushroom burger.
Next door is We the Pizza, also counter service, I have not been there. But if you would be willing to let the kids make a choice......
If you want something more interesting than that, you could hit Singapore Bistro for very simple and inexpensive noodle and bean sprout dishes they do pretty well.
Chinatown Express serves very good steamer baskets of dumplings and their roast meats are quite good. If you go, check out the condiments on the table. They really make the experience. In the window, the y hand pull noodles which look impressive, but they are nothing special.
Good Stuff Eatery
303 Pennsylvania Ave SE, Washington, DC
126 Carroll Island Rd, Baltimore, MD 21220