Grad at 1130, airport 1500, lunch???
1st off I would make a reservation ASAP since a lot of the restaurants in the area will book up fast for graduation season.
There are 3 really good choices near GWU: Blue Duck Tavern, Firefly, or Ris...you should have a lovely celebratory lunch at either. And the bonus is all 3 of these are located in hotels (or next to them) so finding a taxi to take you to the airport will be easy.
Blue Duck Tavern
1201 24th Street NW, Washington, DC 20037