I trusted Stanford Hospital for all three of my surgeries. My surgeon was recommended by my cardiologists and by a friend in SoCal who was a cardiologist.
I do believe the surgeons are the most important, but I also received excellent after care. I should note that when a surgeon gets in there, it can be the unexpected.
I had an issue where they couldn't just pluck the valve in graft off the shelf during surgery. The chief surgical resident hand picked by my surgeon to help him do my 2 surgeon job, had to create a valve in graft just for me during the surgery.
That's the kind of hospital I wanted and I got it.