What is the best way to get there from San Francisco without a car
Probably Caltrain from the City to San Jose and then Uber or a taxi to the museum. You can 'google' Caltrain for the cost, schedule and station locations.
You can take a Caltrain from San Francisco to San Jose which is very convenient. From the station you can take an Uber.
It is very easy to get to the museum if ,you get a bus map of the city of san jose.
It's not an easy commute to get to the museum from SF. It's in a location that is not easily accessible by public transportation. From SF, you'll need to take Caltrain then the bus or Uber as noted by everyone above.
So sorry on my previous answer I indicated museum was in Sacramento California. It is located in San Jose California. the same directions apply as how to get there by train.
Caltrain, but it takes ages! Approximately 3 hours if you continue using the public transport. As recommended below, when arriving to the station (I believe Santa Clara, just confirm) take Uber. You will save more than 30 mins.
I totally agree with the other answers also stop at the J Lohr winery on Lenzen on the way back to the train station for a free tasting. It is also a great place to get a bottle for the ride back to the city.
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