Meadowbrook Country Club is an 18-hole private golf course in Clayton, Ohio, built in 1924 and designed by Alex "Nipper" Campbell. It sits in the $$ (moderate) price range for golf in Ohio. The season runs Feb 1 to Dec 31 (closed on Mondays). Tee times can be booked 1 day in advance.
Details like fees and seasons change, so call the course before you head out.