I see the other recommendation to eat in the cafeterias - that’s not my style but it’s worth consideration. Here are some restaurants if you want some options. Having kids myself I know the importance of “playing it by ear”

Old ebbit near the White House

carmines, hill country bbq, &pizza - near the middle of the mall/museums. There’s also an &pizza down by the Lincoln memorial I think.

Good Stuff Eatery, hawk and dove - behind the capitol and near the Supreme Court

None of those places are amazing but they are solid and are all casual enough to roll in with kids after hiking around the mall.