My wife and I were wanting to move to savannah from Gainesville GA. How much would it cost to live down there? Would it be cheaper than Gainesville?

Look at real estate on zillow.com. Homes will be your only difference, with their property taxes, which can vary a lot by town. Compare with homes in Gainesville.
I have a feeling that Savannah homes cost more, but that's overall, and there are variations in most cities and towns.

I took a quick look and see that homes under 200K are all clustered around the Army Air Field. So I hope you have a lot of money, or don't mind noise.

Savannah is more expensive and depending on where, much more than Gainesville. PS used to live near Château Elan.