Maybe a lot of these places are closed now, but when I lived there in '99...there were a few I visted.
Sharkey's Billiards
Carousel Bowling alley on Ridge Rd. Cleveland. They had a 9 ball tournament on Sunday night. On gold crowns....$15 entry. Calcutta was about $200 for first. Remember Mark Mario hung out there.
Action Billiards on West Rd in Talmadge. You could get action there.
Chagrin Valley Billiards in Bainbridge. May be closed
River City. I remember JR had a high run of 326 balls there.
Ambassador Lanes in Bedford
there were a lot more in the '90's but I know they are closed.