There are many wonderful places in New York City, and one of the joys of homeschooling is that you have time and space to explore them, especially in the middle of the day when many facilities are under-utilized. No list of links comes close to including everything that is exciting in New York (although NYCHEA member Laurie Spiegel's website comes close--Home School NYC), but here are some links that are good jumping off points, along with more general homeschooling links:

Museums
http://www.ny.com/museums/all.museums.html
http://www.library.fordham.edu/researchguides/nyc_musuems.html

Playgrounds and Parks
http://gocitykids.parentsconnect.com/sub-category/new-york-ny-usa/places-to-go/outdoors/playgrounds?sortBy=RATED
http://www.nycgovparks.org/

Libraries
http://www.nypl.org/locations