The truth is there are pretty good bucks in almost area's of the state. Thank the farmers, they're the ones feeding them. That is what you want to do if you're looking for a nice buck, hunt the small woodlots next to farm land. The limited public lands are far too pressured to produce anything of any quality. To have a real chance at a good Illinois buck you have to do either of 3 things over here; 1) lease or buy land. Be carefull it can get very expensive. 2) Use an outfitter. Too darn expensive. 3) Get permission from a farmer. It's tough to get it out of them since they are well aware of how much their land is worth to lease but some farmers will still allow it. You just have to know somebody who knows them.
Your best way is to call the local agriculture co-op to see if they know anybody who would be willing or speak to a farm real estate agent. For a small fee (about $100) either one will hook you up with a farmer with too many deer. Look for farm land near major rivers and adjacent to large woodlots of at least 300 to 800 acres. Those are the areas that produce the real big bucks.
My last recomendation is to learn to archery hunt. The season is much less pressured, significantly longer and the deer are a lot less tense.
Get the land, get the tags, then scout it out big time. Early to mid-november is the hottest time of the year.