Devil's Den is a day hike, and the payoff is the Great Ledge, a slab of open rock above the Saugatuck Reservoir. The ridges climb through oak and maple to reach it. This is the largest continuous preserve in Connecticut, about 1,800 acres and 20 miles of trail across Weston and Redding. The Den opens sunrise to sunset with no camping, no fires, and no dogs, so the van sleeps somewhere else.
That somewhere is Black Rock State Park up by Watertown, about an hour north by US-7 and I-84. Reserve the site before you reserve the van. The campgrounds closer to Wilton are either shut or closed to rigs, so Black Rock is the reliable first night.
Sherwood Island and Long Island Sound
Sherwood Island in Westport is the closest Sound swim, a mile of sand a short drive south and the oldest state park in Connecticut. It's day-use with no campground, and from mid-April through September it allows no dogs, so treat it as an afternoon rather than a night. The overnight beach week and the traprock climb up Sleeping Giant both sit east in New Haven, on the New Haven campervan page.
Weir Farm
Weir Farm sits on Nod Hill Road in Wilton, the only unit of the National Park System built around painting. An hour covers the fields, the stone walls, and Weir Pond that Julian Alden Weir and his circle painted, with the house and studios open for tours in the warm months. It's a stop, not a reason to move the van.
Beyond Fairfield County
North of the New York line, I-684 runs up toward the Hudson Valley, which is worth more than a night or two on its own, and that corridor sits on the New York campervan page. The rest of Connecticut, Litchfield Hills through the Mystic coast, starts at the Connecticut hub. State-park campgrounds here cap trailers and RVs at 28 feet, so if you want something longer than a compact van, the Connecticut RV options cover the bigger rigs.