Were you not in the Navy for very long? It just surprises me at the comment of "once in a lifetime chance to live somewhere else" if you've been in the military. I have a lot of military friends, and they've lived in multiple places around the world by 22. :)
Anyway, it doesn't hurt to randomly go out there. I would, however, suggest you get a plan before moving. With the wonderful thing called the internet, you don't have to physically be in the same state as a job to apply to it or even interview. If you want to go to school, start applying. Either way, you also can start looking for places to live online to get some ideas of options. Research the area where you would be going to. Keep in mind that cost of living is going to be higher in California than it is in Georgia. How much more depends on where you go in the state.
Remember too that moving to California doesn't have to be a once and done thing. If you don't like it or later on find another job you like that's elsewhere, you can move again. I was born and raised in Maryland and never moved out of it as a child, but in my adult life I've also lived in Texas, Hawaii, Japan, and now I'm currently living in Georgia. I'm only in my early 30's too. If you had asked me when I was 22 if I would ever live outside of Maryland, I would probably have told you that I would most likely always be in Maryland. Things change!