Short answer: Yes. New York water is softer than other sources of water, which impacts the gluten in the bagel dough; however, the biggest difference comes from the skill of the people making the bagels. Some New Yorker families have been making bagels for decades.
Long answer: New York City has long claimed to have the greatest bagels in the world along with pizza and other dough based foods. When asked why, they most often point to the tap water of New York City. New York gets the majority of its water from the Catskill Mountains north of the city. These mountains contain very little limestone which adds calcium to water sources. Calcium has a bitter taste that negatively impacts the water quality. After being treated by ultraviolet rays, the water flows down aqueducts and pipes into the homes of New Yorkers. So, does the unique softness of the water impact the making of bagels? Yes...but maybe not as much as New Yorkers want you to believe. Bagels didn’t appear commercially widespread in the U.S. until the 80s, even though they had been made in New York since the 1890s. Most bagels aren’t made with the traditional boiling method, which most New York bagel shops use, because it’s time consuming. However, bagel makers insist that boiling is the only true way to make bagels. It seems that New York water contributes to the uniqueness of NYC bagels, but boiling and skill have far more of an impact.