The League of Shadows has been around a long time (ref: http://batman.wikia.com/wiki/League_Of_Shadows). Its base is roughly halfway around the world from Gotham. However, it seems like they focus their anger on Gotham.
I can't think of any mention (in the Dark Knight movie series anyway) of them attempting to destroy other cities. Yet, in Batman Begins they try to take Gotham down; and in Dark Knight Rises Miranda specifically says she is finishing her father's work.
So: is there really a focus on Gotham, and if so, why? Is there an explanation in the movies or comic books?