You said your home of record/state of legal residence is NY and you are only stationed in VA, correct? Then you will enter NY in the "My Info" area to the question where you lived. Your military pay will not be taxable in VA if you were only stationed there.
Nonresident Military Personnel
Members of the armed forces who are not Virginia residents are not subject to Virginia income tax on their military pay, or on interest received from accounts held in Virginia banks. However, if you have other income from Virginia sources, such as a part-time job, or a business or trade conducted in Virginia, you are subject to tax on this income. Virginia Tax
And yes, if you meet all the requirements then your military pay isn't taxable in NY as well.
Please see What is my military state of residence? for additional information.
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