Water chemistry is only a tiny factor in producing a deliciously crisp and chewy bagel, though the Big Apple's water supply does have lower concentrations of calcium carbonate and magnesium than other metropolitan locales (for the former, it's around 19mg per litres in New York vs 200mg per litre in parts of LA). The harder the water, the stronger the gluten (and the tougher the bagel).
But the real secrets of the classic NY bagel? First, they ferment their dough, letting it sit overnight in wooden containers, growing yeast and producing flavour compounds. Then most of mom-and-pop shops poach their wares before they bake them, a process that gelatinises the dough to make it chewy. To cut corners, the less-loving bagel purveyors brush their stuff with water and baking soda, as you might a pretzel, then blast it with steam.