Check for any unpublished deals or discounts by contacting the airline directly. Sometimes airlines have unpublished fares or exclusive promotions that are not advertised on their website or through third-party booking platforms. By speaking with a customer service representative or checking with the airline's social media channels, you may uncover special offers or discounted fares that can help you secure a cheap flight to New York. Being proactive and reaching out to the airline directly can sometimes yield unexpected savings and opportunities for affordable travel.