Founded in 1916, the Santa Barbara Museum of Natural History is a very low key museum that makes for a great excursion to Santa Barbara with the kids. There are eight exhibit halls with permanent exhibits featuring birds, mammals, insects, ocean life, a planetarium and more. Many of the exhibits are "hands on" with buttons and interactive features that kids particularly enjoy. There are an additional two halls for changing exhibits.
You and your kids can roam the nature paths and visit the well stocked gift shop, full of educational items. I can vouch for the fascination kids (and adults) have at this Museum. It is a very comfortable museum that in my experience is rarely is crowded. The "Museum Backyard" area and gardens has a picnic area, stream, "Dino Dig," and other enjoyable features. The pond and stream often have tadpoles that captivate the kids.
The museum is open 7 days a week and is closed certain holidays. As of January 2016, admission is $12 for adults, $8 for 65+ seniors and teens (13-17) and $7 for children 2 to 12 years of age. Become a Museum member and you don't have to pay for admission. The Museum also offers birthday parties for members. Family memberships are currently $80/year.
Free Family Sundays are on on the third Sunday of January, February, March, April, September, October, November, and December. No free days in May, June, July and August.
Also in the "Backyard" area of the Museum, there is a physical structure managed by the Santa Barbara Audubon Aviary that cares for birds of prey that are no longer able to survive in the wild. Often volunteers will bring these birds out for visitors to admire. These birds are beautiful.