I think it depends on what you're looking to specialize in. Are you interested in a Middle East politics/ policy (or a comparative PhD that includes the Middle East as an area of study)? AUB is very well regarded in the Middle East, but it also has an excellent reputation among academics in the Middle East / Near Eastern field. Not uncommon to find scholars with BAs or MAs from AUB, with a PhD from a top ivy or top public US school. Having said that, most of these come from History depts with a focus on the Mid East.
AUB isn't well known among the general public in the US so you it could go two ways. It might spark some interest or confusion on your resume. For those in the know, I think it's a great addition. I have a friend who's doing the MA you're describing at AUB after doing his undergrad at a top Canadian school and he's loving it. Then again, his academic interests are in the Middle East. Hope that helps a bit.