Hi Bevsdad--I have lived in Boston for 7 years, and moved here from Cleveland. I only lived in Cleveland (downtown and Lakewood) for 3 years, and it was in my early 20's, so I can't speak much to area schools.

But I would compare Shaker Heights and even Cleveland Heights to Brookline Village, or maybe Cleveland Circle...but definitely not Coolidge Corner.
Cleveland doesn't really have any areas with quite as much as you'll find in Boston, but I really enjoyed my time there.
I'd compare Lakewood to parts of Cambridge (although less dense) or maybe Watertown (considering the density factor). Rocky River is a bit more suburban still, maybe more like Melrose or Winchester?
When I was in Cleveland, there didn't seem to be an issue with East Cleveland crime filtering over to SH and CH, but that could be different now.
Good luck to you!