I took the time to do a bit of research on the NYU webpage for the Masters degree you've described. Also, I am quite familiar with the AU webpage from a substantial amount of research I have done on their degree offerings.
Basically, after reading through what your inteded career goals are, I would personally chose the degree from AU. The experience from their faculty appears to be top notch for any career in the International Affairs field that you wish to get into.
Also, NYU masters programs, to my knoqwedge, will be quite stingy in terms of financial assistance (being a TA, RA, fellowships, scholarships, etc). And while I can not garuntee funding for you from AU, I'm thinknig they could offer you a more attractive package to attend.
Given your goals, AU seems like the more practical option given the type of curriculum you are looking for, its prime location, and its APSIA membership (if that matters to you). Also, American's SIS has a great reputation, so there is no need for worries as far as that goes.