These are somewhat in order of decreasing levels of recommendation.
The cog railway up Mt Washington (or the auto road, but I'd prefer the railway myself) is a good option too. Be prepared for chilly and windy conditions at the top...sometimes very, very windy.
The Shelburne Museum is worth a (full) day. The collection is large and very eclectic, including impressionist and american art, a steamboat, historic buildings and interiors, duck decoys, a carousel, hat boxes, and a whole lot more. This is not far at all from the Vermont Teddy Bear factory. Also not too far away is Mt Philo state park, which has a carriage road and pretty easy hiking trails to the top with very nice views over Lake Champlain. (You really do not want to attempt to take your RV on the carriage road!) Also somewhat in the vicinity is the Lake Champlain Maritime Museum, which I haven't seen myself but I understand is a decent museum, though no Mystic Seaport.
If you like hiking, there are heaps of options throughout northern New England, ranging from easy to quite challenging.
The Fairbanks Museum in St Johnsbury, VT is a fun little natural history (mostly) museum, and sort of a museum that time forgot. Some of the taxidermy specimens are usually popular with kids, as are the pictures made from insects.
Canobie Lake Park in Salem, NH is a fine medium-sized traditional amusement park.
The Montshire Museum a little north of White River Junction is a decent science museum geared towards children. (The name comes from verMONT and new hampSHIRE.) It's not really much different from many other fine little museums scattered around the country, so I would skip it before some other things.
If you're interested in tools, there are a couple of museums in Vermont that are good stops. The American Precision Museum in Windsor has a lot of machine tools. Kitty-corner across the state, there's the (free, but only open on Saturdays) Arnold Zlotoff Tool Museum at the Apple Island Resort in South Hero, which has an impressive collection of antique hand tools.
