On roads with narrow outside lanes or where a bicyclist travels at roughly the same speed as motorists, take the lane. It's your right, and your responsibility, to decide when it is safe for the motorist to overtake you. The key to riding safely is to behave as the operator of a vehicle. This is the philosophy used safely by cyclists across the country for decades. Off-road urban trails are often terribly dangerous.
Nearby roads are much safer.
The Bay Area is a highly developed urban area. There is no car-free paradise waiting to be found. Cars aren't going anywhere. Cope with it. Teach yourself to be a better cyclist, and encourage others to ride smarter.