The closest airports are Paso Robles, Santa Barbara and San Luis Obispo Airports but it's unlikely you'll find direct flights there. Most people combine a visit to Hearst Castle with some other California sightseeing. If you want to do Northern California sightseeing, fly into Monterey, San Jose, SFO or Oakland; if you want to do Southern California sightseeing, fly into one of the LA area airports: LAX, Burbank, Ontario.
Hearst Castle's website has some info: hearstcastle.org/plan-your-trip/…Edited: 05 April 2018, 23:55
San Luis Obispo (SBP). It has daily service to LAX, SFO, PHX and SEA. Most people fly into the LA or SF area airports and drive up as part of a larger trip. San Luis Obispo is more than four hours’ drive from larger cities in California.
I would NOT take a bus. Rent a car. The bus service is infrequent and could take hours.Edited: 06 April 2018, 00:53
There are also connecting flights from LAX to San Luis Obispo on American and US Air- it is about an hour's drive from the SLO airport to San Simeon if you rent a car. Paso Robles is a private airport. If you came into SLO and got to Paso Robles (about 1/2 hour north of SLO) there is a tour to Hearst Castle through a company called The Wine Wrangler that picks you up at your hotel in Paso.
This thread is a month old. The OP never came back to tell us anything else about their plans, or even so much as a thank you. Annoying.