May want to try Shaker Badminton Club, not sure if the place is still open. Here is the link with contact info. http://shakerbadminton.blogspot.com/
There is another one in Mayfield Heights ,Lander Elementary School. Reach out to AK ,akapinos2002@yahoo.com Play on Mon,Wed @8pm and Tue @8.30pm For professionals, Shaker could best fit...Talk to Dave,dbcumming@JonesDay.com, the Club leader.