You need to file a New York State (not City) return. New York does tax you because the activity was performed in New York. Georgia also taxes you, but will give you a credit for the tax you pay to New York on this income.
Where your clients are actually from is not the determining factor, but rather, where the activity took place. Since you were in New York State, you pay tax to New York state on this activity.
New York City does not tax you, however, because NYC does not tax a nonresident of NYC (which is part of the NY State return)., even though the activity was performed in NYC.
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