Skokie Country Club is an 18-hole private golf course in Glencoe, Illinois, built in 1897 and designed by Donald Ross. It sits in the $$$$ (splurge) price range for golf in Illinois. The season runs Apr 1 to Nov 1 (closed on Mondays). Play is generally limited to members and their guests.
Details like fees and seasons change, so call the course before you head out.