New School University
The New School for Social Research was founded by rebel Columbia professors who decamped from Morningside in 1919 after whining that Nicholas Murray Butler had stifled their freedom to dissent during World War I. The professors included Charles Beard, John Dewey, and James Harvey Robinson.
Rubbing shoulders with NYU downtown, the rechristened New School University remains very outside the academic mainstream. That hasn't stopped it from being in the pop culture mainstream, however - the dean of the poorly named "Parsons The New School of Design" is best known for hosting Project Runway.
It even retains its tradition of protest - in 2008 students attempted a pale imitation of Columbia's 1968 brouhaha by occupying a university cafeteria and then demanding the police surrounding the building bring them vegan options while they debated their next step. The protest ended in apathy as winter break descended on the school, and was subsequently declared a great success.