April 16 (Bloomberg) -- Columbia University, New York University and Barnard College, three of Manhattan's most competitive private colleges, are drawing record applications, and the reason goes beyond demographics. New York is increasingly a magnet for students who want corporate internships and a chance to tap the city's deep well of entertainment offerings, students and educators say. Fear of urban crime and terrorism, once barriers for some applicants, has diminished. Major crime in New York is down 66 percent in the past 10 years, according to the city's police department. In March, the Princeton Review Inc., a test-preparation and admissions...