Backcountry campsites in the lower hudson valley new york area?

I am looking to bring my family on a true camping experience this summer far away from technology. I have previously been camping in the adirondack and such places but I fear that treks in such areas may be to tough for them. However I want them to have a true back country time. So if anyone is aware of a state or national park that is fairly easy terrain, short distances between sites, and within a few hours drive of southern New York please share.