I am not sure what you like to do, but if you had a rental car, Solvang and Santa Ynez are only about an hour away. Excellent shopping, wine tasting (many excellent vineyards reside in Santa Ynez) great restaurants and beautiful scenery. You could spend the morning exploring Santa Barbara and then drive to Solvang for lunch and wine tasting and still have plenty of time.
If it is your first visit to Santa Barbara, then you could easily spend the entire day there, as well.
Tom
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