Definitely don't take my experience as the gold standard, but...looking over the bios of the people here where I work, only 2 went to Syracuse (one is my boss, actually!) While I don't believe that has anything to do with the quality of the school, I think it does have to do with the alumni networks here in DC. That's just my feeling, though. There's a decent-sized California contingent here as well, though this is spread out between USC, Berkeley and UCLA (with a few others in the mix: Davis, Santa Barbara, etc).
The breakdown by school also has to do with the ability to get an internship your second year and, quite honestly, students who are from DC schools can easily sign up for part-time spring or fall internships (which are much, much less competitive than summer internships) which can lead nicely into full-time positions. It most certainly doesn't mean that people from out of the city can't also get internships, it's just that the reality is that spring and fall internships are much less competitive and, therefore, easier to land.
But here's the real moral of the story: if you're a great student at a well known international affairs/policy/development program, with significant quant and qualitative experience AND have overseas experience (I cannot emphasize this enough), you'll be just fine.
Maybe I should look into counseling programs! That would free up my job for one of you...