Depending on what jurisdiction your case is in (e.g. Atlanta municipal court or Fulton County State Court), you might be able to keep this off of your record through a pre-trial diversion program.
As far as punishment for public intoxication goes, you are probably looking at a combination of fines and community service. If you are concerned about this going on your record, you may want to seriously consider getting an attorney to represent you.
In response to your question about punishment for being intoxicated in public in Atlanta, if there is a pre-trial diversion option available, you are a great candidate for such a program.
I am not sure about Fulton County and Atlanta, but in some of the neighboring counties, you have to have an attorney to be admitted in those programs, so you may want to check into that ahead of time.
As previous attorneys noted, if you are in Fulton County, you should easily be able to enter into their Pre-Trial Intervention program (PTI). The Solicitor will dismiss your case on that day and you will be required to enter into the PTI program and complete whatever guidelines/requirements are set forth.
Once you complete these requirements, you can apply to have your record expunged. This will completely remove the case from your record. If this is an arrest outside of Fulton County, you still should have this available to you. I would definitely ask the prosecutor wherever you are.
I would suggest you hire an attorney to navigate this process as PTI/expungement can be a little complicated if you do not know what you are doing. Keep in mind though this is a misdemeanor so the most you can face is 12 months in jail and generally a $1,000.00 fine. However, this is pretty much unheard of for a first arrest, especially for one of Public Intoxication.