I would not recommend living in graduate housing at NU there are much better options in the same price range near campus (evanston place, rental homes, etc.) I would personally not live as far as Chicago, though you can try downtown or south evanston to find a cheaper place closer to businesses, etc. The purple line is not terribly reliable and commuting can be a pain in the cold. The shuttles run pretty frequently, but again, commuting during rush hour is a pain, snow is a pain, etc. I think walking is the way to go in Evanston.
My disclaimer: I did my undergrad at NU, so my experience has been a little different, But i did commute between chicago and evanston often and found that it sucked the life out of me.