There is no such bank in GA anymore. Ga. has one of the highest bank failure rates in the US. Just make sure the bank is insured by the FDIC and you don't have more than $250,000 in any one name ($100,000 after Dec. 31 unless they extend it). Or try a credit union. The Lockheed credit union is open to nearly everyone (residents of Cobb Co., etc etc) in the Atlanta area. It's now the LGE Community Credit Union, www.LGEccu.org. The Delta credit union, now Delta Community Credit Union, https://www.deltacommunitycu.com/, is also open to most anyone. I think as a whole credit unions are managed more conservatively than banks these days.
Here's a web site that independently evaluates banks. I think it's hard to plod thru, but it may help. You can check the banks near you.
http://www.bankrate.com/rates/safe-sound...
