My perception of the Bay area is much as Silvaire describes.
Last time up there, I flew into RHV, who were very accommodating and got a good deal on car rental from the FBO. Going out however there was a big delay getting IFR release because of the traffic from SJC being very close, and it being Friday afternoon. VFR is a lot easier.
Livermore and Tracy are not far away and are less affected by the Bay area fogs and marine layers. I know someone training at Livermore and most of his instructors are Stanford professors. Rates are a bit lower than the Bay too.
Hayward seems quite a good base, but I've no knowledge of rental or training there.