Take the Staten Island Ferry. Great views of lower Manhattan from the deck. Fare is free! Very, very crowded during rush hours (your son can tell you when these are) - but ferries run 24 hours/7 days week, so you should be able to get in a round-trip (takes about 1 hour or so) sometime.
Empire State Building observatory for a 360 degree view of NYC and surrounding areas. Statue of Liberty (accessible by boat only). Carriage ride through Central Park. High tea at the Palm Court, Plaza Hotel in Manhattan. Lots to do and see. Wear very comfortable shoes and do not carry a large handbag! I always use a fanny pack or a cross body small messenger type bag when in NYC. (I grew up there).
Mood Fabrics- 225 West 37th St., NYC (Project Runway shops there). They do sell "cottons", but not sure if they are quilting cottons or what. They have a web site and toll-free number if you want to check prior to your trip. Other than that, I think someone already mentioned Gotham Quilts.
Have a great time in NYC! It is an awesome city.