Between 1991 and 2001, the number of students living in N.Y.U. housing tripled to 12,000, from 4,000, as the university raised its national profile. (In the early ’90s, 50 percent of its students came from the metropolitan area; now that figure has declined to 10 to 15 percent.) By 2031, N.Y.U. expects its total student body to grow to 46,500 students, up from the current 41,000.
Things are a bit different in really big cities, but as someone who has spent time/taught at various universities I can say that those with a significant residential component - even in big cities - are substantially different, and probably better for students, than those without.