The Holocaust Museum Cafe is not kosher, but there are sealed kosher products (e.g., parve sandwiches, noodle salad) available in the cafe that were brought in from a kosher caterer. There are also things like sealed bags of chips (OU) on sale at the cafe. Make sure to check for the seal on the sandwich, as the cafe serves similar products that are NOT kosher. Many of the cafe staff are aware of the issues, and can help steer frum customers to the right stuff.
Eli’s is a great meat restaurant in the District.
The largest frum communities in the DC area are in Silver Spring, and there are a larger variety of shuls and kosher restaurants in Silver Spring and Rockville (to the west), some of which provide kosher sukkos.
A good resource for any Jewish traveler to the DC area is the Washington Vaad’s (capitol k) Web site (just Google Washington Vaad and you’ll find it). They provide a list of all Vaad supervised establishments and a list of affiliated shuls.