Beechmont Country Club is an 18-hole private golf course in Beachwood, Ohio, built in 1923 and designed by Stanley Thompson. It sits in the $$ (moderate) price range for golf in Ohio. The season runs Mar 1 to Dec 20. Tee times can be booked 7 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.