Vermont has some nice state parks, too.
If you like to hike, Mt Ascutney might be a nice choice. The hike up from the campground would be challenging for most 5 year olds, but not necessarily impossible (about 4.6 miles / 7 km long, 2500 foot / 750 meter elevation gain). There is also a road up to the summit. At the top there's a network of shorter trails (with vistas), an observation tower, etc. Paradise park in Windsor, not too much of a drive away, is a pleasant place to spend an hour or two or three walking around.
Smuggler's notch is another neat area. The campground is a little drive from the notch proper. I would not take a large RV through the notch (every year a few people manage to get themselves wedged up there), but a car or minivan or similar vehicle is no problem.