I am applying to Marshall, but I can tell you there are plenty of places to live in the area.
I recommend River West, West Loop, South Loop, Ukranian Village, Bucktown, Wicker Park, Lincoln Park, and Jefferson Park, in that order.
I've lived in the city proper for 8 years now - there is plenty out there.
I rent in River West and pay $850 a month, and that includes a garage. There are loads of apartments within walking distance to public trans in that price range. I can be at JMLS in 20 minutes by public trans, maybe less.
Best of luck.