Water in New York is quite expensive and especially in the summer months it can prove to be too costly for your budget (a 500ml bottle can be found from $1 to $4).
So a good solution is to fill your bottle from drinking water fountains that you will find in several parks, museums and shops. This water is potable and you can consume it without any problem.
You can also get large packages from a supermarket and have them at your hotel (we bought from Duane Pharmacy, which is everywhere, $7 for 24 bottles).
Toilets are also a problem you may face. There are public toilets in many places. Some are crystal clear while others don’t even come close. Take advantage of the toilets in the museums, restaurants, shops, cafes and bars that you will definitely visit during the day. All the toilets we entered, at the above points, were incredibly clean.