The 2014-2015 school year will start on Thursday, September 4th, and end on Friday, June 26th. In between those two dates are Thanksgiving Recess on Thursday, November 27th, and Friday, November 28th; Winter Recess, from Wednesday, December 24th through Friday, January 2nd; Mid-winter Recess, from Monday, February 16th, to Friday, February 20th (includes Washington's and Lincoln's birthdays); and Spring Recess, from Friday, April 3rd, to Friday, April 10th (includes Good Friday, Easter, and Passover.
See the full calendar on the NYC Department of Education website here.