As a former "resident" of SB, I think what makes the most difference would be what you'd plan to do before/after the game. The drive from Chicago is approx. 2+ hours, tho it would be shorter from the southern burbs.
OTOH, staying in SB would allow you perhaps easier access to tailgating and a couple of beers after the game without the need to drive.

Staying in SB shouldn't be too dificult if you plan ahead, but my own personal choice would be a hotel in Chicago, with many many options to choose from
Best wishes.