You have all mentioned most of the places I'd suggest - good call on Bullfeathers, shinerbock! If you're going to Old Town Alexandria,
Gadsbys Tavern is great place to have lunch. It's good for dinner, too, but it's the exact same food at double the prices. There's a small museum there, and needless to say, George Washington hung out there.
Since you're taking the kids, they would enjoy
The Silver Diner.. I'm only familiar with the one at Tyson's Corners, but it's fun for the kids.
One of my favorites is
The HillwoodMuseum. It was the home of Majorie Merriweather Post (heir of the Post Cereal fortune), and she designed it to be used as a museum after her death. There's lots of Faberge, incredible artwork, the Hapsburg Wedding Veil - lots of things like that. You can have High Tea on the premises. One restriction is that all children must be over six.
If you're into Lincolnalia, PM or email me - there's SO much to see on that angle, and I don't want to bore anyone. I wouldn't even bother with the White House unless you have the personal tour - you'll feel like the Griswolds in
European Vacation.
And by all means, let me know how it goes - I'm in charge of a convention there next summer for a lot of people who have never been to DC, and I'd love to hear that perspective!