Having lived in California and Georgia, I can say that people will be more friendly and social here and while the culture is somewhat different, I doubt you will find it shocking.
Some considerations though:
1)Georgia has a winter. People who move down from the north or over from the west coast assume south = always warm. We're not southern Florida. I've made a similar mistake whenI was in Monterey, CA - I figured it would be similar to Southern California and I wouldn't need a jacket (found out I was wrong the first week I was there!).You'll need a jacket here, and some sweaters too!
2)Also if you have allergies, GA is about to go through what I call the green month, basically a month where everything is covered in a yellow-green layer of pollen. I noticed a thin layer on my car yesterday signaling its arrival.
3)You will find people who will embody stereotypes of the south, but not everyone here is the same. Not everyone who lives here or grows up here has a southern accent.
4)Fort Gordon is located in the Augusta area. This means people from all over the country who work on the base live in the area. This isn't just soldiers, but also retired veterans, government civilians, and contractors. Fort Gordon is home to the Signal Corps (every vehicle needs a radio and someone has to secure the communications) and a major NSA facility (Signals Intelligence).
5)Augusta has a lot of things to offer, and what it doesn't have can be had with a reasonable drive. Atlanta is 2 hours west on I-20. Savannah is about 2.5hours SE.