Idlewild and Banklick just outside of Cincinnati are both excellent courses, but if you're only going to be in Lexington, here's what I think of the courses there.
Shillito is a fun, straight forward course that's lightly wooded in areas. The front 9 is shorter with lots of birdie opportunities while the back 9 is a little longer and more challenging. There's a walk from hole 9 to 10, so you should take a look at the map or print it out before you go.
Veterans Park is a much more challenging course than Shillito. It is mostly wooded with some tight fairways and a few long, tough holes in the back 9. There are a few long walks between holes here so bringing a map with you is a MUST.
If you're really looking for a challenge, Riney B is just a few miles south of Shillito. It's got 24 holes and is 1/3 wooded and 2/3 open. The open holes are mostly long and challenging with tree-lined fairways and punishing rough. The wooded holes are difficult to say the least. Some have twisting fairways while others challenge you to throw perfectly straight, so bring your A game. The layout is easy to follow, but because they've recently added more holes, the numbers on the signs pointing you to the next hole are incorrect, so printing the map isn't a bad idea.
Lake Mingo is a fun little 9 hole course just a mile away from Riney B. It's fairly short, lightly wooded and has strategically placed OB on many holes. It's a great place to get your a warmed up in preparation for Riney B's long holes.
