Umm, 5 guys is a hamburger chain that is basically equivalent to eating at Wendy's or Cheeburger Cheeburger. Fine and all, but really, why travel to DC to eat at a place that is located in mall food courts? If you really want 'American' as far as cheeseburgers go, go to a local place like Old Glory in Georgetown or Ray's Hellburger in Clarendon (Arlington, VA).
In Georgetown there is Zed's, which is Ethiopian and pretty decent. Some people love it, it wasn't much my thing, but I still enjoyed it. And the setup of how you eat there is neat.
Not quite as 'different' but we LOVE Cactus Cantina, which is Mexican as you might have guessed. It's fairly close to the National Zoo and their food is great and it's very kid friendly. I haven't met anyone who doesn't like it so far.
For Italian, Pasta Mia is incredible and walking distance from the zoo in Adams Morgan. They're open at 6:30pm except Mondays and Tuesdays and a line forms around 6pm everynight.
Specifically for pizza, which I know may sound lame, 2Amys is great. It's actually certified by Naples as having authentic pizza. It's also pretty close to the zoo, right next to Cactus Cantina actually.
ETA: The American Indian museum does have a good food court with actual 'ethnic' foods, not the standard museum food court stuff. But I wouldn't go there specifically for the food, only if I were visiting the museum anyway. And we've gone a few times but its not the best museum for small kids. There is a lot of reading to do an not so many hands on exhibits.