I love the Hudson River Valley, but there's not a lot there for kids.
Cities have cool museums, but not much camping. Although you might be surprised. There's a nice campground inside the DC Beltway. DC is kind of far from you, but you can stay in the
Greenbelt campground for $16/night, and take the Metro into downtown to see the free Smithsonian museums.
I'd offer to let you stay with us, but we really don't have the space, and it wouldn't go over too well. But I'd meet you for lunch if you came. Give you plenty of tips for sites to see.