San Francisco Airport First in the U.S. to Reach Deals With Uber, Lyft
mashable.com
mashable.com
Nashville airport was the first in September. They even proactively created a ride share symbol.
AirBART is the shuttle bus service between OAK and BART. http://en.wikipedia.org/wiki/AirBART
However, the ideal transportation if you're visiting is to simply walk around. It's amazing how easy it is to walk everywhere in SF.
For Alcatraz, just grab a lyft/uber to the pier and take the ferry. By the way, if you have time the longer, late evening tours are quite interesting.
And also sold out months in advance.