I've had a few tires patched over the years at various places.
I wouldn't worry about which place does it, I've never had a bad result.
The only thing I'd worry about is how nicely they treat your rim. I'd tend to favour a small Mom and Pop shop where you can talk directly with the technician so you can emphasize that you want the rim treated nicely.
Nod, I got the silver color chipped off (about 1/3 by 1/2 inch area) on my Team Dynamics 1.4 by a major chain tire shop. If they hadn't been my racing rims, as versus my pretty rims, I would have blown a gasket. But they were flawless before the chip. Should you ever have a shop mount your wheels in the future, show up with a torque wrench in your hand, set to 77 foot pounds. Most shops want to use impact wrenches to tighten your bolts/nuts. Their attitude is "tighten them till they squeal", which damages things.