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Flight
All Bay Area airports will put you within an hour to Livermore, but SFO has a little more of a drive. SFO tends to have more flights available.
Flight
OAK is closer to Livermore by a good 20 minutes and tends to be cheaper, too. Less flights tend to be available.
Train
You can grab the train from both SFO and OAK and get all around the Bay- but especially to Dublin, which is only 15-20 minutes to Livermore (and the venue). From SFO: Take the Red (R) line from the airport to Daly City (4 stops), where you'll want to get on the Blue (B) line. Once you're on the Blue line, hang tight all the way to Dublin, which is the end of the line! From OAK: From the Oakland airport, take the Blue (B) line to Dublin, which is the end of the line. Before getting on the Bart, you will want to find a pay station, where you can get a Clipper card. Or, you can download the BART app and use Tap and Ride. Fares for the BART depend on distance, but the approximate fees (based on the Fare Calculator) are: SFO-Dublin ~$15.35 (one way) OAK-Dublin ~$13.15 (one way)