Circa Foggy Bottom is a favorite among young professionals and GW grad students alike. The patio scene here is almost always hot, perhaps due to the inevitable snowballing of people that happens when a bar is located at the mouth of a metro stop. Don't just come for the drinks; the cuisine is top notch and priced well.
Circa Clarendon and Dupont also sport great patios.
[Circa Dupont] [Circa Clarendon][Photos via, via, via]