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The Amtrak train station is close to everything so you don't need to worry about a car at all.
Taxi between station and hotel.
25 cents Shuttle bus runs 2 routes along beach front & along State Street (shopping, dining, entertainment).
Municipal buses are good too.
Land & sea tour shows you the sites around town and harbour, and many wine tours can pick you up from your hotel for free.
There's a bicycle rental place on the opposite side of the station from the train tracks, and a short walk across the plaza/parking area.
For much of Santa Barbara - the beaches, the downtown and other commercial areas - you have the choice of all these types of transportation because it's quite flat. So your time is your only big limitation. But if you want to get up in the hills, renting a car is the best option, by far.