Hi, C.
This is going to be a VERY difficult time of year to find a 'quiet' store, but we have found the Shops at Willow Bend Mall to be VERY quiet during the week! (Maybe you can take your son there soon, before the Christmas shopping really gets in "full gear", because then NO PLACE is going to be "quiet".) :( Did the dr possibly recommend maybe using ear plugs to help dampen the noise when you are out with your son? How does your son handle being in the nursery at Fellowship? Do they have someone who can take him out of the room if his room gets too noisy for him?
I will stay on the "look out" for quiet stores or places and let you know what my husband and I find.