Is it possible?
sure. Picking a neighborhood close to the right public transportation would be important.
http://www.northwestern.edu/uservices/transportation/commuter/public-transit.html
If your actual home is in Chicago, it is probably doable. If you are just renting or something, it would probably be a hassle.
You should post this in the NU page. If you’re a grad student, it’s normal. If you’re undergrad, you’re missing out on a WHOLE LOT by not living on campus. If you can afford it, which you probably either have enough money or enough financial aid, then you should live on campus / in Evanston.