Hawthorne CC is one of my favorite Clev east side courses. I'm not a pro, but not a beginner either. Hawthorne has never been overbooked when I'm there, so they space the times well, and the other golfers tend to keep a good pace. Like most courses, there's a few holes that are more gracious, and a handful that are tight or have challenging greens to keep you sharp and engaged. Great course. I've also played a fun scramble there, and all the guys had a blast. Not too pretentious, but not too casual either.
Enjoy!
(Definitely not any sort of paid advert here, just a guy that likes golf and saw that Hawthorne needed a few reviews on Yelp. I'm happy to encourage you to golf there.)