I've lived in San Francisco for my whole boating career (limited though that may be at 3 years). There's a couple of Class IV and V options within 2.5 hours of the city. There's also a fun Class III river (South Fork of the American) that has guaranteed recreational flows on weekends throughout the year so you'll always have AN option for boating the entire year!
I'd recommend checking out this website for a better idea of what we have out here in fabulous California: The Tip of the Iceberg
. The Northern Sierra rivers are gonna be the closest ones to California.