I moved to Chicago after college @ 21, to go to Columbia for Grad school.
I agree you don't need a car if you live in the downtown student housing, or find an apartment in a safe neighborhood near a train/bus line.
South Loop is fairly safe, just be smart (don't stay out tooooo late at night), walk with your head up, be confident, and aware of your surroundings!
The Columbia students are usually always out and about near the Columbia buildings especially when it is nice out. You will love Chicago.
Good luck & Enjoy!