Q. What state(s) would I need to pay taxes to for those 2 - 3 years?
You are weaving a tangled web that could result in double taxation, as you could be considered a resident of both states, in which case you may not be allowed a credit for tax paid to the other state.
Once you move to NY, you are clearly, for tax purposes, a resident of NYC and NYS and must file as a NY resident (the year of the move[s], you file as a part year resident of both GA and NY). The fact that you intend to stay more than one year is a major factor.
This forum is not the correct place for car and drivers license and voting rules. That said, my experience is that you should be changing all those to NY.
