Sharpe Reservation is located in the middle of nowhere in Fishkill, NY. It offers New York City kids an opportunity to enjoy nature in the summer. During the year, schools and youth groups can participate in the education programs available. It is a 2000+ acres of nature with cabin accommodation - but not for the general public who are looking to camp there. (If you are the leader of a scout troupe, I highly recommend you try organize an overnight trip for your troupe there.)
That does not mean you should give up in checking out this wonderful place. For once a year, they open the grounds for the general public during their Maple Celebration in March. And it is worth bringing your kids to this all-day event if you are camping/traveling in the neighborhood. http://www.freshair.org/maple-celebration
I have taken my daughter and friends there for a few years and it is always a fun-packed day to cure cabin fever before all other places are open for activities before the start of spring: watch a sky show at the planetarium; make crafts in the nature discovery room, play outdoor games designed for different ages, taste maple syrup from competing makers, watch maple sugaring demonstration, enjoy a BBQ lunch, touch an exotic animal, or walk the many trails on the ground. There is also local handmade goods and foods for shopping. (TIP: There are several screenings at the planetarium during the day, but it is best to be there at the earliest shows when there are not many people; otherwise, you probably will have to line up for half an hour to get in.)
The activities are spread out over at different locations within Sharpe Reservation, so wear comfortable shoes. But it is such a nice break from winter and such soul calming environment that I highly recommend it.