I believe Flynn had some connection to the Standard Oil folks in Cleveland. If memory serves, when that same group was looking for an architect for their winter retreat in Florida, they also retained Flynn. Thus, Cleveland Heights in Lakeland was created. It is now a muni run by the City of Lakeland. The original eighteen was eventually turned into 27 by the City but there is still some Flynn there...although it is hard to see in most spots. Some of the greensites on the original holes are pretty cool.
As for Cleveland courses, I can only echo what others have said. Sleepy Hollow and Manakiki are very good. Hawthorne Valley (Ross) is now public and well worth a play. Fowler's Mill, an early Pete Dye design for TRW Corporation, is also good and very much the low profile Dye that you find at places like Harbour Town and The Golf Club. Unfortunately, my understanding is that it will close after this year.
On the private side, I love Canterbury and Kirtland. The last four holes at Canterbury and the back nine at Kirtland are sublime. As most have said, Brookside is terrific but Canton is a good hour drive south of Cleveland. Sand Ridge in Chardon is a very good Fazio. I have not been to the Country Club yet but it is on my to do list.
If anyone does put together a day at Manakiki and Sleepy Hollow, let me know. It would be well worth the drive from Columbus.