Once you are no longer a resident of New York state or have income from NY state, then you will no longer be liable for NY state taxes, even though you may return to NY occasionally to visit.
As a US citizen, you will however still be subject to US federal income taxes on any income you earn worldwide, so even when you move to Poland, you will still be required to file a US tax return to report any income you have.
Once you have been out of the country for 330 days, you will qualify for the foreign earned income exclusion which will allow you to exclude $87,600 from your foreign earnings before any tax might be due to the US.
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