Great to know that you're into Middle Eastern history! I don't know of many History programs with a strong Middle East emphasis, but I can recommend several universities with Middle Eastern Studies departments that often work closely with faculty in history departments - NYU being one of them. You might also consider lesser known schools such as the University of Arizona and the University of Utah. Both of these schools offer great language training, if you don't already have it. Arizona, for example, offers Arabic, Persian, Hebrew, modern Turkish and Ottoman Turkish. There MA program is pretty good if you want to use it as a stepping stone into PhD programs in history. Also, there funding is pretty good. Utah, on the other hand, I've heard has bad funding, and actually got denied Title VI funding for FLAS fellowships this year - something to consider.
Big name schools to consider are definitely - Princeton, Chicago, NYU, Michigan, Columbia, Berkeley, and UCLA. What are your specific interests, and time periods? That might help you narrow down your choices. Anyways, best of luck!