I lease right at 600 acres and have hunted Southern IL exclusively since 2013. A lot has changed over the years, mostly the quality of the deer. Don't get me wrong, there are still big deer in the area I hunt, but they aren't as many as there once was. It has become very challenging to see one over 150". It has reached a point to where the cost of leasing along with other expenses do not justify hunting the area if looking for 150's or better. Now if you are looking for 120" to 140" deer that will be a reasonable expectation and you should see some bucks in that score range and if you are lucky something bigger may stroll by. Since IL has legalized the use of crossbows and most recently certain calibers of rifles, I suspect the quality will continue to suffer.

I am of the opinion public land will offer you a better opportunity at a better quality deer. There is in most cases a larger amount of land and some bucks simply avoid being killed and get older. I have got to old and just not that mad at them to put in the work on public that it usually takes to find the above average quality deer. If I were younger there is no way I would pay what I do for a private lease in the current times.

Like many above noted and to answer your question anytime from end of October through November you can expect to see rut activity. My favorite week is Novemebr 6th -13th. The break between the first and second season can be really good. Also if you can locate a good food source late season can be awesome hunting.