Wow, awesome culture clash that you'd even ask this!
Yes, the bay area, but particularly SF is extremely anti-car. This is probably rooted in environmentalism, but in the city it also resonates with many people for health, social, and economic reasons.
The sentiment is so strong among younger people that if people own a car they will often almost apologize for it in friendly conversation. Like "yeah, I still have my odd beater from when I lived in LA... But I have free parking at the office and it's nice for carpooling to burning man".
From a personal perspective, I grew up in orange county, but moved to NYC in early adulthood and SF later. I own a car and a motorcycle. I love riding the motorcycle, but bicycling or walking is frequently more efficient in the city, not to mention pleasurable.
If you have only ever lived in car-centric places like so cal, I rely strongly recommend taking a long vacation in a walkable place like NYC or a European city where you know people who can show you the ropes. You might be surprised how much you enjoy Not driving.