My turn to shine! I volunteer with the New York Rescue Mission, which is the oldest homeless shelter in America. We're in Tribeca, shelter almost 200 homeless men and women each night, and feed well over 400 per day. Right across the street from us is NYU's Lafayette Hall, which houses over 1100 students. I can't remember us running into any issues. AFAIK neither does the Bowery Mission, our "sister-shelter" in Manhattan. That isn't to say, of course, that no one who EVER uses the shelter services commits a crime, just that it's incredibly rare.

Shelters are basically impossible to organize these days because the NIMBY pressure is so difficult. It kills property value.

FWIW, I work with our residential program residents at the Rescue Mission, and I can say hands-down that absolutely no one I know there would cause any uptick in crime. The vast, vast majority who come through the door are great people who have just hit some really shit luck and circumstances in life and are trying to put things together. But, of course, most are also people of color, which scares wealthy white people.