The Cleveland Orchestra is world class, and Severance Hall (their home) is very close to CWRU.
For theater, you have the Cleveland Playhouse which is amazing.
In addition to these, there is the Rock and Roll Hall of Fame…everytime we’ve been there, some excellent local group has been playing.
There are concert venues for all kinds of music…and Blossom Music Center (you would need a car) in the summers.
Plenty of other theater too.
CWRU actually has relationships with four different hospital groups. University Hospital main campus is located right there. Cleveland Clinic, Metro, and the VA hospital also have ties with CWRU.