Here are my favorite public tracks in Cincinnati/Northern KY area...
1.
Stonelick Hills
...by far the best course in the entire tristate area.
http://www.stonelickhills.com/
2.
Lassing Pointe
...the website doesn't do the course justice. #18 has a 101 yard green...completely different hole one day to the next. Awesome place to play.
http://www.boonecountygolf.com/
3.
Legnedary Run
...designed from classic holes around the world. Had some green issues last year, as did many courses in the area.
http://www.legendaryrungolf.com/
4.
Shaker Run
...absolutely great course (27 holes), however, the greens were in horrible shape in early April. They are under new management so hopefully things will turn around. If it does I put this course right behind Stonelick Hills.
http://www.cincigolf.com/shakerrungolfcourse.htm