Two good resources:
Ohio Golf Guide is a website with user reviews of every club, public and private, in the state and has top 25 rankings of the best public, private and 9 hole tracks based on user reviews. There are also clickable, county-by-county maps that bring up a list of all the clubs in a particular county - so say if you were going to the Hocking Hills, the Lake Erie Islands, etc. you could find courses nearby. I like this website quite a bit - user reviews display the individual users' biases, but don't have some larger political/economic motivation like publication rankings. Check it out!
Golf Cleveland Ohio has reviews of all the public courses within an hour or so of Metro Cleveland, many/most with pictures. The reviews aim to be pretty comprehensive, and even though I always don't agree with what they say (I think they miss the mark on my home track, for example) I value their imput and the fact that they have extensive photographs for most of the courses. Another one to check out.