Best Buy has been trained by Apple. They have complete service manuals, use genuine Apple parts, Apple diagnostic software, etc.
You might also have another shop or two authorized by Apple in your area. You can find a list of Apple authorized shops in your area using this link:
Find Locations
Might be a good idea to call the store or shop in advance though, to make sure that they have the battery that you need in stock. In most cases, you will be in and out in less than an hour, but you might have a few errands in mind in case the shop is busier than normal when you arrive.
I usually drop the phone off and then go get some lunch and run a few errands, then pick up the phone.