Exmoor Country Club is an 18-hole private golf course in Highland Park, Illinois, built in 1896 and designed by H. J. Tweedie. It sits in the $$$ (premium) price range for golf in Illinois. The season runs May 1 to Nov 1 (closed on Mondays). Tee times can be booked 8 days in advance. Play is generally limited to members and their guests.
Details like fees and seasons change, so call the course before you head out.