I live in New York but I’m from the South, and so I’ve heard of both High Point and Pace but am unfamiliar with Mary Washington (I only know about it because I knew someone who went there; we did a summer program together). However, familiarity isn’t necessarily a good thing - I can’t say I have a particularly high opinion of Pace.
Pace has a slight majority of NY students; 44% are from out of state, but I am betting that most OOS students are probably from nearby states. They are also very diverse, with less than half the student body being white. The vast majority of Mary Washington students are from Virginia, and the university is considerably less diverse than Pace. Most of High Point’s students are actually from out of state, but High Point is the least diverse of any of your choices, with 84% of students identifying as white.
The other thing to think about is that Pace is a true urban university; they don’t really have a traditional campus with grassy areas where people play Frisbee, etc. Now, it IS located in a prime NYC location - right near City Hall, at the base of the Brooklyn Bridge. Personally, I would not have wanted to been an undergrad in NYC, but if you really want an urban undergraduate experience Pace is the place to be it. Mary Washington and High Point both have more traditional type campuses.