Born & raised in North West Ill & now live in N.E. Iowa one hour from Ws..
Ill.-South-Shawnee National Forest. Crap Orchard.

Go to Ill. DNR web site & look at public areas for the section of the state you want to hunt.
Bowhunt is your best bet-lots less pressure for sure.
Don't let the word public scare you. If you don't get an Ill. permit go to Ws. Plenty of excellent Deer Bowhunting there-been traveling to Ws. many years & always public ground. Lots of National forests.
I usually Bowhunt the upper 1/3 of the state.
I have never gun hunted for any biggame animal & this is the start of my 51st year Bowhunting. Good Luck.