You won't need a car in Evanston, but it can be convenient to have one. It's a very walkable town and, assuming you're living near campus, you can walk to most things you need. Some shopping centers are further away, but there are buses you can take. I had a car and only used it a few times a week: for grocery shopping so I didn't have to shop at the Whole Foods (there's a Jewel but it's a little further away), and occasionally on weekends to go places. It also came in handy for driving to campus for those winter night classes when the temperature dropped.
Looking back, for me it was worth the extra cost, but plenty of my friends didn't have a car and it didn't bother them. For those few times when you would need one, there's a zipcar in Evanston and/or you can borrow someone else's car.