If you want to be really close to the airport here are some public golf options:
Kentucky (25 minutes or less to the airport):
Kenton County Golf Courses (27 hole facility, decent but not great golf, affordable)
Boone Links (18 holes, good golf, affordable)
World of Golf (18 hole executive course, bare-bones experience in quality of turf and design, cheap)
Devou (18 holes, conditions can be rough at times but some cool views, OK value)
Twin Oaks (18 hole course, basic golf course - nothing memorable, cheap)
Normally, I would recommend Lassing Pointe but there are only 9 holes starting 9/18 due to a renovation.
Ohio: (again under 25 minutes from airport)
California (18 holes, good value, conditions are normally decent)
Reeve’s (18 holes, situated next to a private airport, private jets and single prop airplanes buzz the fairways - very cool, extremely flat, cheap)
If you want to drive a little longer (40 minutes or less from the airport), the Links at Rising Star (Indiana) and Legendary Run (Ohio) are good options.
Let me know if you have additional questions. One more thing, use Golf Now to book as some of these courses get even cheaper on a hot deal ($28 w/ cart for 18).