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While I was in the San Francisco area I rode BART, Caltrain, Muni, and VTA. I stayed at the Day's Inn in Burlingame near the airport and used both Caltrain and BART to get to and from the City. I also rode Muni while in the City.
The main railfan things I did were to ride the entire VTA light rail line and look at the construction of Muni's new Third Street line. Most of VTA's light rail is either on exclusive rights-of-way or in reservations in the middle of the street. But there is a portion in old downtown San Jose that evokes trolleys of the "classic" period.
The new Third Street line is going to be as long as the existing Muni light rail lines. The northern end is finished except for the overhead. The southern end is completely finished. It's the middle portion that is still under construction.
Caltrain is a very heavily utilized commuter route, mostly two tracks with numerous grade crossings. Only near South San Francisco is there room for four tracks that enable express trains to bypass local ones.
The BART extension to the airport is very good but rather expensive. Once when I wanted to visit friends in Walnut Creek it took over an hour to get there from the airport, and that was a direct route with no transfers. It gives an idea of just how large a system BART is.
Trust me, I totally enjoyed my stay in the Bay area. If I were independently wealthy I'd move there in a trice.