Tony Cheng's is one my favorite restaurants in Washington. It's hard to miss; TC's in the middle of Chinatown, right across the street from the metro. The Mongolian BBQ is on the first floor, so don't mistake it with the seafood restaurant upstairs.
The atmosphere is very formal, but I see tons of patrons in jeans and sweaters, so I'd say dress upscale casual. It's family-friendly, and a lot of fun for little kids to watch the chefs tossing around their meal on the large grill. Be sure to try the warm rolls with some of your meal; after, you're treated to oranges and ice cream. I don't know if I'd call it authentic, but the chefs are good, and they are the ones who decide what spices go in your food. If you have any allergies, be sure to speak up, otherwise they'll assume all spices are fair game!