The simplest solution would be if your employer will withhold VA taxes in addition to the NY taxes. Virginia will give you a credit for the taxes that you are paying to NY which will reduce much of your tax liability to VA. However, any additional income that you receive [i.e. dividends, interest, etc.] would only be taxed to VA, so if that is a substantial amount, you will need to factor that amount into your VA tax liability.
If your income is fairly stable, you can make an estimate of your VA tax liability by using the partial year tax return percentage from last year to calculate an entire year.
