The OP asked about parking shops. The original question said nothing about it being a valet parking location, nor did it say that it was a hospital. I did a small city parking location (self-park) last week and they reimbursed for up to 3 hours. For parking. Nothing else. I see lots of hospital parking shops withing 20 miles of me. Some are valet, some are self-park. Generally, the ones which are going to incur a fee for parking require a stay of 30 to 60 minutes. Some hospitals near me offer free value parking. I have not done any of them because they require that you stay somewhere in the hospital for 30 to 60 minutes and they pay a $10 fee and allow a $2 tip. The $2 tip would be fine ($1 in, $1 out), but the $10 fee is not enough to compensate for the time spent there, the time writing the report, and the mileage.
I did manage to get lucky and snag a few about 3 years ago when I had to go pick up medication for a friend at a hospital in NJ. Free valet, and I had to be there. So, I made a little money while being a good friend (she was a hospital employee, therefore had to use the hospital pharmacy (= free prescriptions) and with a a newly broken ankle, 8 new screws, and a new plate in her ankle was not forced to go there herself after the first visit. Due to laws governing certain narcotic pain pills in NJ, they could not prescribe more than 7 days at a time.
Shopping Southeast Pennsylvania, Delaware above the canal, and South Jersey since 2008