NEW YORK — Nurses at two of New York City’s largest hospitals went on strike Monday in a dispute over pay and staffing levels after a weekend of negotiations did not produce a deal for a new contract. The walkout involves as many as 3,500 nurses at Montefiore Medical Center in the Bronx and about 3,600 at Mount Sinai Hospital in Manhattan. Gov. Kathy Hochul urged the union and the hospitals late Sunday to take their dispute to binding arbitration.