I was excited to hear that the AMC Huts are going open for the 2021 season (with COVID mitigation policies in place). This is one of the easier huts to get to and is absolutely family friendly and a great introduction for anyone to the world of backpacking. The best part being that you can take limited gear in since the hut provides beds (bunks with mattresses, pillow and wool blanket) and breakfast and dinner.
The hike in is almost entirely flat through the forest and a beaver pond and finishes with a brief ascent up to the hut. It's also great for cross country skiing in the winter. The hut itself consists of two large bunk rooms with beds that are stacked 3 high (try to keep young ones on the 1st or 2nd beds) and a common room where meals are served. There are also composting toilets and potable water available. The hut (in non-COVID times) can get quite full and be quite loud. Be sure to bring some ear plugs!
The falls are just a short distance from the hut and worth a visit. There are several day hiking options as well as the ability to extend your overnight adventure to other camp sites in the vicinity. If you cans wing the price, it's worth visiting at least one of the huts in the AMC's White Mountain system.