Santa Rosa Regional Airport (STS) is 1/2 hour away. Direct flights are available on Alaska Airlines from/to Los Angeles, Portland, San Diego & Seattle. You can easily rent a car in the airport (http://www.sonomacountyairport.org).
Oakland International Airport (OAK) is about 1 3/4 hours away.
Sacramento International Airport (SMF) is about 1 3/4 hours away.
San Francisco International Airport (SFO) is about 2 hours away.
Bus & Car Services from the Airport:
The drive to Villa Mimosa is lovely. So most guests prefer to rent a car at the airport and enjoy the picturesque views as they drive up the valley.
You can also catch a bus from SFO or OAK and rent a car in Napa or Santa Rosa cities.
Evans Transportation offers both SFO & OAK airport bus services and car pick up services (http://evanstransportation.com/).
Airport Express offers bus service from SFO and OAK to the Santa Rosa Airport where you can rent a car (http://www.airportexpressinc.com/).