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 New School remains very outside the mainstream. It even retains its tradition of protest - in 2008 students attempted a pale imitation of Columbia's 1968 bruhaha 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.