What you describe is, apparently, a change in employment. The fact that you have elected not to move, makes it a personal situation and the expenses are not work related. Generally, your "tax home" is the entire city or general area where your main place of business or work is located, regardless of where you maintain your family home.
The situation where it would be deducible is when your work in GA is directly related to your current job in NY, and the GA assignment is only temporary (expected to be less than 1 year). That is, you are on an out-of-town assignment for a job based in NY.
So, unless you can describe some specifics that redefine the circumstances, nothing is deductible. For example, if your job in GA is not as a W-2 employee, but on a freelance basis. Even then, the answer is only maybe, depending on other details.
