Charles M. Schulz Sonoma County Airport: The closest airport, but still about a 45-minute drive to Sonoma in normal traffic. Rent a car at the airport if you are visiting wineries; rideshare/taxi works only if you are staying around the Plaza and have winery transport booked. There is no quick, useful airport-to-Sonoma rail link.
San Francisco International Airport: Rent a car and drive north via US-101, Highway 37 and SR-121; allow roughly 1½–2 hours, longer on Friday afternoons and Sunday returns. A private transfer or rideshare can spare you driving after a flight, but it is expensive; public transport is bus-heavy and poor value for a short visit.
Oakland International Airport: A rental car is the sensible option: roughly 1½–2 hours via I-80 and the Napa/Sonoma approach, traffic permitting. Do not choose OAK expecting an easy public-transit connection to Sonoma.
Sacramento International Airport: Useful mainly if flights or car hire are materially cheaper. Drive about 1¾–2¼ hours, depending on Bay Area traffic; a car is effectively required.