Alaska State Museum - Even if it isn't a rainy day, a visit to the Alaska State Museum is fun. The Alaska Natives Galleries have a beautiful Frog and Raven House, Athabascan quillwork clothing and birchbark canoes, Tlingit ceremonial masks and hats. Check out the life-size bald eagle nest and wildlife dioramas leading to the second floor.
On the second floor, in children's area kids can take the helm of the ship Discovery or try on historical costumes, and don't miss the gold nuggets necklace, ore cart, and collection of minerals.
Mount Roberts Tramway - Ride the aerial tram up to the top of Mount Roberts, with a viewing platform for panoramic views of Juneau, the Inside Passage, and mountains in the distance. At the top, take the one mile Alpine Loop Trail, marked with totem carvings on the living trees. The tramway ticket also includes an 18 min. movie about Tlingit people and history.
Whale watching cruise - Go on a two or three hour whale watching cruise in the waters around Juneau, to see humpback whales, orcas, Dall's porpoises (black and white like the orcas), and sea lions.
Last Chance Mining Museum - If you have a car (or get a taxi), go for a short drive on Basin Dr. to the Last Chance Mining Museum. Situated in the woods, water cascading down the steep mountains into streams where you can still see old sluice boxes, it's easy to imagine the first gold prospectors.
Buy a gold pan in the museum, and take it down to the creek down the hill to pan for gold (the shallow areas of the stream are best).
The Museum itself is full of big mining equipment (early 20th century), fascinating for all the engineering-minded members in your family.
Project Playground - An amazing playground, with elaborate climbing structures, swings, and slides, barbeques and covered picnic area, plus a small lake and swim area for little ones. The playground is on the highway north out of Juneau toward Auke Bay, at the Channel Dr./Salmon CreekTrail Rd. turnoff (you can see the playground from the highway).