Mission Santa Barbara - "Queen of the Missions," Mission Santa Barbara was founded in 1786. The church you see is actually the fourth church, dedicated in 1820 (the first and second churches were smaller adobes, the third church fell down in an earthquake in 1812). At the mission, the friars and Chumash Indians grew crops, planted fruit trees, tended cattle, sheep and horses, made cloth, tanned leather. A water works (still in use today) provided irrigation and water for the mission.
Stop into the church (ornamented with two bell towers, the only California mission with two towers), then also explore the mission kitchen, friar's bedroom, and garden quadrangle next door.
In the cemetery (with skull and crossbones over entrance), an unmarked grave is where"Juana Maria" is buried. Juana Maria, a young girl who lived alone on the Channel Islands, was rescued by a sailing ship and came to live at the Mission Santa Barbara - the book Island of the Blue Dolphins is based on her life.
Museum of Natural History - This museum is a super introduction to the wildlife and native people of the Santa Barbara area. Check out nifty dioramas of local birds (including the California condor) and mammals, grizzly bear, foxes, bats, cougars and cultural dioramas about the Chumash Indians. Outside the museum, check out the large white skeleton of a blue whale, and cross over Mission Creek to walk down the nature trail along the stream.
Rocky Nook Park - After you've visited the Museum of Natural History, bring your lunch and picnic under the oak trees. Rocky Nook Park is right across from museum and has lots of picnic tables. To run off a little energy, climb on the sandstone boulders, play in the playground or take a short hike up the trail.
Alameda Park - Alameda Park has an awesome playground, called "Kids World," with a large castle play structure, swings, slides, and picnic tables, plus lots of grass and shade trees. If you have a toddler, this is a "must play."