Georgetown seems like an obvious reach possibility, George Washington and American for less reachy possibilities (note American is big on demonstrated interest).
Fordham maybe? And Loyola and Marquette. Yes, more Jesuit colleges, but they tend to be good for what you are describing!
Edit: I realized after DC I sort of ignored your regional preference, which is de facto because the SE happens not to be a great place for the type of college you are describing. But, Tulane and the University of Miami could be worth checking out.