Yes, you will need to file a Virginia return. You will file a Virginia nonresident return because you have business activities in Virginia. Both Virginia and NYS will tax you for your income you earn there, but NY will give you a credit on your tax return for the taxes you must pay to Virginia on the rental income you earn there.
If your LLC is registered in Virginia, you will want to stay current with any business filings required in Virginia to maintain your LLC. Be sure to answer any appropriate questions in TurboTax about your Virginia requirements. For more information on this from the state of Virginia, please see this FAQ: https://www.scc.virginia.gov/clk/befaq/forinva.aspx
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