Canterbury Golf Club is an 18-hole private golf course in Beachwood, Ohio, built in 1921 and designed by Herbert Strong. It sits in the $$$$ (splurge) price range for golf in Ohio. The season runs May 1 to Oct 31 (closed on Mondays). Tee times can be booked 30 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.