If the year were 1987 I would recommend Performance Aircraft of Hayward, only becuase I worked there then
The Bay area is a big place. Where you live will have an impact on where you might want to do training. If you live in San Jose, for instance, you wouldn't really want to go to a flight school in Oakland. The drive to and from would make you crazy, especially in rush hour traffic.
It has been too long since I worked in the area to recommend a school. What I can do is talk about the different airports and the advantages or disadvantages of training at them. Even that may be a little dated as the traffic has changed a bit.
I quite like Reid-Hillview airport as a base for training. The early aviation pioneer, John J. Montgomery, did some of his glider tests at a hill just south of the airport. It is a G.A. only field. The advantages are that it is relatively easy to get to a practice area in a short amount of time and you have the instrument approaches of nearby SJC for practice. Hayward is good for the same reasons, although it is a little farther to get to the practice area and it is closer into the Class B airaspace. Oakland is okay, but it is a co-use airport with lots of airline traffic. It would probably be difficult to do practice approaches there nowadays. Livermore would be good as it is the closest to the practice area and has it's own instrument approaches. I would stay away from Palo Alto and San Carlos for a training base.