I love the Santa Barbara Museum of Natural History. This is a very low key museum that makes for a great excursion to Santa Barbara with the kids. The Museum was founded in 1916 and is very quaint and fun to roam around. There are 11 exhibit halls with birds, mammals, insects, ocean life, a planetarium and others. Many of the exhibits are "hands on" with buttons and interactive features that kids particularly enjoy.
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 had tadpoles in our most recent visit that captivated my kids.
There is a stream in the back area The museum is open 7 days a week and is closed certain holidays. Admission is $10 for adults, $7 for seniors and teens and $6 for kids (free for kids under age 3). Or become a Museum member and don't pay for admission. The Museum also offers birthday parties for members (it only costs $75/year for a family membership).
In addition to the permanent exhibits, the Museum features other exhibits of interest. In Fall 2008 the Museum had an exhibit entitled "Giants - African Dinosaurs" that featured life size replicas of African dinosaurs and actual dinosaur bones.