Do researchers at schools that publish good journals get priority in publishing in those journals?
The answer is certainly not - not officially anyhow - except insofar as being a well known mathematician (which someone who is at a place like Princeton typically is) makes it easier to get one's paper accepted to a fancy journal. That effect is likely real (though of a magnitude that would be difficult or impossible to measure, and hopefully not too large), but it typically applies on a more global level rather than a journal-locale-based level.