1) your own copy/pasted stats show that NYC has 61.3% of the children and are getting 63.6% of the money
2) Defining NYC/LI as Bronx, New York, Richmond, Kings, Queens, Nassau, and Suffolk counties (see http://www.censusfinder.com/mapny.htm) and using the census's 2008 estimates by county (http://quickfacts.census.gov/qfd/states/36/36001.html) shows that NYC has 11.2 million people, and 'upstate' has 8.3M, which gives NYC 57% of the people.
3) Using the same websites as above shows that when you define a child as anyone between 5 and 18 years old, NYC has 57% of the children.
4) So I accept that your number of 'eligible' households and children is correct as per the stipulations of the actual bill - definitions are obviously different, but there's no way to slice this that shows NYC/LI are getting an unfair share of the $ if you use published numbers.