hi saiarun_9
Unfortunately 9/11, and you are right, alienated some people against some people and vice-versa in the globe.
GRE is required not only for non-USA citizens but also for USA citizens too. There is an exception rule not written anywhere. Let say: you have two patents of inventions in your pocket I guarantee you no one will care if you ever took GRE test but automatically are cordially invited.
To tell the truth the better you score on those the better are the chances towards your own goal. I think this is rule of thumb. As far as suggestion what universities that matters not. Write to any of it. Just do consider your monetary issues.