1. go look at the Old Mission Santa Barbara
2. check out the inside of the Arlington Theatre (you can go inside when no movie is playing)
3. visit the Santa Barbara Courthouse Docent Tours and climb on top of the tower (free, closes at 3pm)
4. check out State St and all the cute/colorful courts and shops
5. Try the "Sea Salt Cream and Cookies" flavor at McConnell's Fine Ice Creams (really, don't miss it!)
6. walk through the Santa Barbara Certified Farmers Market (Tuesday afternoon or Saturday morning)
7. take a walk in the Santa Barbara Public Market
8. try the macaroons at Renaud's Patisserie & Bistro in front of the Arlington Theater
9. take a look at Casa de la Guerra
10. try the coffee at Handlebar Coffee Roasters
11. walk down to Stearns Wharf and try to guess where North is before getting to the end of the pier (there is a compass)
12. have a great lungh/dinner at Santo Mezcal
13. walk around the boats at the Santa Barbara Harbor
14. go to Shoreline Park and watch the sunset from the beach
15. have lunch with your feet in the sand at Shoreline Beach Cafe
16. go play some beachvolley at East Beach
17. walk on the sand to Butterfly Beach
18. go get a drink at sunset at Belmond El Encanto
19. go for drinks with friends somewhere in the The Funk Zone

Here's the few I make sure to always do when I'm up there:

Brunch at the Four Seasons Resort The Biltmore Santa Barbara.  Dinner at San Ysidro Ranch.  Cocktail at Joe's Cafe.  Any meal at Hendry's Beach.  Singing, card tricks, and the cajun martini at The Palace Grill.

If you want to be a tourist and see a lot fast, hop on the Landshark with  Land & Sea Tours. They take you around town on an open air amphibious vehicle and then into the harbor -- boat ride! It launches a few times a day from Cabrillo Street (not to be confused with Carrillo or Castillo streets) by Stearns Wharf. 

Bike along the waterfront. Maybe bike into Montecito and have a meal at the Four Seasons Resort The Biltmore Santa Barbara 

As Andreas said, wine tasting is great.

I also recommend a stop at the Santa Barbara Public Market. If nothing else, have either Enjoy Cupcakes, Santa Barbara or Rori's ice cream while there. Or consider picking up a picnic's worth of stuff -- fresh break, cheese, salami, and again, cupcakes, and take your treats to the beach or a pretty spot like Alice Keck Park Memorial Gardens

If it's a pretty day (and when is it not?), go to the top of the Santa Barbara Courthouse Docent Tours to take in the view of the red tiled roofs and snap some photos to make your friends jealous.

I would go wine tasting in The Funk Zone (off of state Street by the train tracks) . Lots of nice wine bars with tasting menus.

With a bike you can travel almost everywhere in Santa Barbara. Start with a cruise down State Street Route to the beach, turn left, and ride along the beach bike path to the beach volleyball courts. The path continues on the other side of the street, winding around the bird sanctuary and zoo, then crosses past the cemetery, and continues on the ocean-side of Ty Warner's mansion, all the way to Butterfly Beach and the Four Seasons Resort The Biltmore Santa Barbara and Coral Casino Beach & Cabana Club. You can do the round trip in about one hour.