If you don't happen to have an Apple Store nearby, you might have a Best Buy store in your area to handle the battery replacement. Another option would be an authorized Apple service shop.
You can find a list of authorized Apple service locations in your area using this link:
Find Locations
Best Buy and the local shops don't require an appointment for a battery replacement, but it would still be a good idea to call in advance, if only to make sure that they have the battery for your phone in stock.
Unless the store or shop is really slow when you take the phone in.......unlikely.....plan to drop the phone off and pick it up a few hours later that day. The shop will give you a time when the phone will be ready.