I did find this on the Georgia Department of Labor website:
"If you reside in Georgia and have not earned Georgia wages in the past two years but earned wages in another state, go to a GDOL career center to obtain information for filing a claim against the proper state. We will also register you for employment services."
http://www.dol.state.ga.us/js/regular_unemployment_insurance.htm What it comes down to is if you haven't actually worked in Georgia during the time that they would be looking at then it might just make your life easier to file in one of the states that you have worked in. They will have conditions that they will outline for your scenario (living in one state, filing under another state).
Any job that had you fill out a W-4 when you started and sends you a W-2 at the end of the year will count towards your unemployment coverage. You'll need to have at least the companies' contact info when you go to start your claim, and preferably their federal identification number (which you can find on the W-2 if you have it).