You were a part-year resident of NY (and NYC) - for the period 01/01/2020 - 06/30/2020.
All the income you earned while living and working in NYC is subject to NYS (and NYC) tax. The fact that your employer was based in Boston does not affect your NY tax responsibility; you are subject to tax based on where you physically performed the work.
When you complete the Personal Interview:
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Select Florida as your "state of residence" (as of December 31, 2020);
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Answer "Yes" when asked if you "Lived in another state in 2020?"
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Your "Previous state of residence" would be New York.
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The "Date you became a resident of your new state" Florida) would be the date you moved to FL with the intent of staying (07/01/2020).
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When asked if you "Earned money in another state?", answer "No" . You have already told the program you were a resident of both NY and FL, so it will know you are subject to tax from NY (FL has no state income tax).
