The short answer to this question (and this assumes you otherwise have a viable wrongful termination claim) is yes, you do have a duty to mitigate your damages for breach of your employment contract in New York. On the positive side, though, your former employer will bear the burden of proving that you failed to mitigate your damages, as that is an affirmative defense to your breach of contract claim.

For additional information on this topic, please see "Breach of an Employment Agreement & the Duty to Mitigate Damages in NY."