It will depend on when you were charged for and convicted of DUI. If it was in the last five years, then the USCIS likely will find that you are lacking in good moral character--you can fight this but it may be easier to wait to apply for citizenship until five years has passed since the DUI occurred. I would recommend that you consult with an attorney who practices in NEW YORK and can tell you how the New York USCIS looks on this issue.
In order to answer this question it will be necessary to review the criminal records regarding your DUI conviction. While DUI is generally not considered to be a crime involving moral turpitude, a conviction during the required period of good moral character can still be held against you. You should consult with a qualified and experienced immigration attorney who can review the specifics of your case with and advance you of the issued involved and the options available to you.
I practice criminal law in Queens County, N.Y., the most racially diverse county in America. Many of my clients are Green Card holders or have no status at all. Thus, I deal with such immigration issues every single day.
You must be very careful when deciding how to dispose of your DWI matter because certain convictions can affect your ability to become a citizen and/or cause the revocation of your Green Card. In New York, DWI (Vehicle and Traffic Law sections 1192-2 and 1192-3) is an unclassified misdemeanor and WILL give you a criminal record and probably will delay your ability to become a citizen. However, the lesser charge of Driving While Ability Impaired By Alcohol (DWAI) is a violation and will NOT give you a criminal record or affect your immigration status.
Make sure that you consult with an experienced criminal defense attorney before resolving your case!