I don't know anything about the visa you may be granted to study in the US, so purely a calendar answer:
There are traditionally three vacation periods in the US academic calendar:
The end-of-year holiday break, centered around Christmas, Hanukah and New Year's. This may be a couple of weeks or longer than a month.
Spring break: Usually a week long, sometime in March or April. This can be a great time to escape miserably cold universities.
Summer break: While most PhD students are not "off" in the summer, it is easier to travel because taking and teaching classes is less common. Summer break usually lasts from May or June to August or September. Many conferences take place in the summer, however.
Some universities also give a whole week off for American Thanksgiving or have a week-long fall break, but this is less common. I would also strongly recommend not traveling by air aroundMany Americans travel home for Thanksgiving unless critically necessary, as airports and domestic routes can be very busy. As a commenter mentioned though,which may complicate or even make a flight to Europe might not be that bad if you can get ittrip home easier.
That said, if you are not doing research that requires your presence, or are able to take classes virtually, PhD programs can be very flexible in allowing you to continue your studies and work while not in your city. However, the pay is probably not high enough to allow you to take many trips home (especially since Georgia isn't a huge travel destination for Americans like say, London or Paris).