agree with 11/5-11/13 ish..
shot mine on Nov 7 2008
they say for the midwest, Nov 7 +/- 2 days are the best 5 days of the year. Most midwest deer have approx the same schedule. It is a bell shaped curve of course when it comes to anything, and Illinois has little pressure so can be good most of the season. I would go prior to firearm season.
this is of course if the weather cooperates.
2008 season was great around Oct 30 with the cold front, stunk when it warmed up, and then Nov 7 it cooled down again and things got heated up. even in the warm weather they were moving, but at night or very low light in the AM/PM.