Domicile Question

The address you put on your tax return is the address you want the IRS to mail any correspondence and/or a check should they need to mail your refund.  The address you put on the tax return does not determine what state you are a resident of.  If you do not intend to return to the state you left to move to Georgia then you are a Georgia resident.  You would file a Georgia part-year resident tax return and do the same for the state you left - if they have a state income tax.  

Let's go back.  

You relocated.  If it is your intention to make GA your permanent home, then you are a GA resident, regardless of where you are living at the moment.  Domicile is significantly based on intent, and if you abandoned your previous domicile with the intent to remain in GA, then you are a GA resident.  The special rules for statutory resident only apply if you live in GA more than 183 days but you want to consider yourself a permanent resident of a different state.

This is also to your advantage most of the time.  If you are a permanent resident of your original state (state 1), then you owe a tax return to state 1 as a full year resident that reports and pays income tax on all your worldwide income.  You ALSO owe a non-resident tax return to Georgia that reports and pays tax on income while you lived or worked in Georgia, even if Georgia was not your permanent home.  State 1 will usually give you a credit for taxes paid to Georgia to offset double taxation.  However, if you relocated with permanent intention, then you are a part-year resident of state 1 and a part-year resident of Georgia.  You report and pay state 1 income tax on all your world-wide income up to the date you relocated, and you report and Georgia tax on all your world-wide income you received after your relocation, but you aren't double-taxed in either state. 

If, on the other hand, you intend your state in GA to be temporary and you still consider state 1 to be your permanent home and you intend to return to state 1 at the end of the temporary assignment, then you are in fact a permanent resident of state 1, where you file a return and pay tax on all your world-wide income) and you are a non-resident of Georgia and you file a non-resident return to pay tax only on income earned while living or working in Georgia.

In any case, the address you use is where you want to get mail from the IRS, if they need to contact you.  It does not have to be any place you live or have lived.  It could even be the address of a trusted friend or relative if you are between permanent addresses,