If you were convicted of DWAI (Driving While Impaired by Alcohol), VTL 1192(1), a violation level offense and the most likely reduction, then you have not been convicted of a crime. There are implications in regards to your privilege to drive in New York and possibly other states with this charge. You likely owe fines and surcharges to the court, and will possibly have to pay administrative fees to DMV to get your license or right to drive in New York reinstated. If you have a license in another state, that could also have been affected. You might want to check your driver's record in your home state.
On most job applications, they ask whether you have been convicted of a crime, not whether you have been arrested for a crime. The answer to that question, based on what you have said, is "No." A normal business should get a criminal history sheet that might not reflect lesser offenses. If your application is to a federal agency or a criminal justice agency, they will likely be able to receive a more complete criminal history, and you may be required to provide a more complete explanation. It is best not to misrepresent such matters if you are undergoing an FBI check for some reason.
DISCLAIMER I do not practice law in your state. This answer is provided solely for general informational purposes only. This answer does not constitute legal advice, create an attorney-client relationship, or constitute attorney advertising.
Most jobs will not ask if you have been arrested but rather if you have been convicted. It should only matter what offense you plead guilty to or were found guilty of that matters.
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