The closest airport is the Santa Barbara Airport (SBA).
Los Angeles (LAX) and Burbank (BUR) Airports are the next closest and a quick 1.5 hour drive north to SB.
Arriving by Car:
From Los Angeles Area: 1.5 hour drive north from LA
From San Francisco: A scenic 5 hour drive from SF
Arriving by Train:
This fun alternative is great if you don't feel like renting a car and have a few extra hours. Amtrak has several stops in the LA area that head north to SB. The SB station is in the heart of downtown and close to several hotels.