What a fun adventure is in store for you should you take on this mission. @JLeslie hit the nail on the head with Charleston and Savannah if you want the 101 course on Southern Hospitality. Both cities are lovely with lots of things to do, but they cater to the tourists.
If you want to dive right in to reality, then just pick a state and go visit the small towns. Since I grew up in Virginia, I’ll use it as an example. Here is a list of Virginia towns with less than 1000 residents. Once you have your travel dates picked, you can look through this list of Summer Festivals in Virginia and see if there are any of interest to target. They are always a good way of experiencing the local lifestyle.
If you drive, then then take some of the “off the beaten track” routes instead of the highways. You’re more likely to run into the Mom and Pop diners, shops, and motels. Avoid all chains, unless you truly need a break from the southern culture. Be brave and try the local cuisine.
Most importantly, take photos and keep a journal or create a blog. It will be one adventure of your lifetime that you won’t forget.