The Maine Huts & Trails system includes 4 off-the-grid huts connected by miles of well-maintained trails. The huts generally have a big lodge for meals and relaxing (with lots of board games available), plus one or more separate bunk houses divided into smaller units. The bunks are sparse but you'll only be there to sleep anyway. The huts have a "full service" season where there's a full staff to cook and keep things clean, and a "caretaker" season where you're pretty much on your own. The open/closed status of the huts has fluctuated in the last couple years, so it's important to do some good research before heading out.
We've had excellent family trips to both the Flagstaff Lake Hut and the Grand Falls Hut. We prefer to go during caretaker season when prices are lower and the huts are far less crowded. It's like backpacking without having to bring a tent. You can use the hut's commercial kitchen, but you have to bring all your own food, seasoning, etc. One hint: Aim for a June trip on the last weekend before full-service season. You'll get great weather along with a nearly-empty hut. Kids love having the run of the place, and sleeping in bunk beds is always exciting.
The Flagstaff Lake Hut is accessed by a mostly flat 1.8-mile trail, much of which follows the shore of Flagstaff Lake, and it features a nice swimming area and good paddling. One time we even paddled a couple miles in and arrived at the hut by canoe. The Grand Falls hut is a slightly longer but easy/moderate hike in (2+ miles) from the Lower Enchanted trailhead (only accessible in the summer). For more of a challenge you can also hike in from the Big Eddy trailhead with 7.8 miles of mostly flat trail. From the hut you can hike to Grand Falls (1ish mile), which is an exciting waterfall with great places to play in the river. We've done these trips with kids ages 3 to 11.