Cumberland Trail does have nice greens and is a pretty good course. It doesn't make my favorites list because I don't think the course (outside of the greens) is anything special. Add to the fact that condos come into play too much (I actually have to hit my ball over the corner of a condo on the short dogleg right hole) and draw it back to the fairway is a little goofy. Also the beer rule they have is horrible for them. (where you can only have beer on one side of the course that is divided by a road, but it's not divided by the 9's).
Kyber Run is a solid course for the money, and the Links at Echo Springs is up there too. So is Westchester, Darby Creek, Champions, Royal American, etc, but they really aren't my personal favorites. :) I do play all of them though and enjoy it.
Clover Valley can become a long round due to all the tall grass there on every single hole. But if you are a decent handicap golfer, Clover Valley is probably my favorite layout in central Ohio for public courses. I was a rules official for the High School Girls district golf tournament a couple years ago and the round was well over 6 hours for them. Many of the girls simple were not good enough for the course. I do not recommend Clover Valley for high handicap golfers, they'll hate it. And I also recommend playing Clover at off peak times, but I don't blame the management for that - it's just that everyone is searching for their balls for too long in hazards. Not much management can do to police that on a busy day.
Chapel Hill can also become a very long round as #7 eats golfers alive and there is often a 3 group wait on that hole which backs everything else up. I'd also avoid peak times there too.
No course is perfect, but the ones I listed I think are some of the best overall courses in central Ohio.
I haven't been to Eaglesticks in ages.... I'll have to make that trek again soon!
Never been to split rock - I'll check it out sometime.