The Watergate Hotel is sort of off by itself. The nearest dining/bar activity outside the hotel is about 6 blocks away. Probably a cab ride in late Dec.

Restaurants are quiet during that period, as congress and lobbiests go home.

High end dining is on 21st street, above K in NW. plus Cittronel in Georgetown, and Kinkaids near 21st.

Lots of interesting mid priced places on M st in Georgetown, both eating and bars.

Adams Morgan, 16th at end of first alphabet has a lot of ethnic restaurant. Washingtoh has a number of Ethiopian, Meskerem is considered best.

I don't think there is anything close(walking distance) to Watergate that is open late. Washington is not a particularly active late night town, except for the very loud 20ish crowd.

Might try the bar in the Watergate(I assume there is one) upon arrival for food, quiet, and drink. There should be food serviced by the restaurant kitchen. The restaurants in the watergate have had their ups and downs of late. I have not dined in the current version. It once housed the most famous, and best restaurant in DC.

The Old Ebbit Grill downtown and Bistro Francais in Georgetown are open late.