Sandy Hook is inaccesable from NY. Plus it's too close to VOR 31L 31R approaches at JFK. The begining of the approach is Kings Point which is at the tip of Sandy Hook. The approach takes you over Canarsie which was one of the airports that lost out to the airspace overcrowding some 20 years ago. Now it's just a Police helicopter base.
The Eastern LI site you are talking about, I believe, is Calverton the old navy base. It's an environmentally sensitive area with with plane hating granola eating folks who won't let it happen.
Calverton is a good 2-3 hour drive from NY with the daily traffic.
There's no realestate or airspace to build a new airport in the NY area. We already have FRG, HPN, EWR, JFK, LGA, and Teterboro all with converging airspace. It's the most complex and congested airspace in the country and you want to add another airport?
If anything LGA should be closed. JFK could be further developed The existing land mass can be built out into the Jamaica bay with landfill where additional runways can be built. No one lives out there. However it is a protected bird estuary. But birds can be poisoned.