Autozone can see why the check engine light is on and all Autozone locations should offer this service for free.
Although Autozone will check why your check engine light is on it's not a complete diagnostic like a real auto shop would do.
What Autozone does is plug a tool into your computers system on your vehicle and then go into the store and print out an error code list on what could be causing the check engine light to come on.
A real auto shop can do a more thorough test on the vehicle to pinpoint the exact cause of the check engine light or any other engine or electrical problems but Autozone can just check for some problems and give you possible causes.