I was thinking about doing this, or more precisely, thinking about trying to talk someone who has a boat into doing it. Kind of interesting - it's always difficult to imagine that the serene waters rolling along under the tree-lined banks of the Sacramento connect to the cold and choppy Bay. (For more on this feeling, see McElligot's Pool.) It might be good fun to start in the city and see how far you could get.
I went looking to see if anyone had done this from SF, and still couldn't find evidence of that. But there used to be a race - not from SF but from Stockton (starting on the San Joaquin) all the way to Redding, prior to the dam. I can't find anything showing the event is ongoing, but this 1957 Popular Mechanics article describes it. In those days the winner would make the 316 miles in 7.5 hours.
Still no evidence online that someone has done it from SF, but that would make it about 350 miles and a long weekend.
6.5 (6.4 miles/ 10.3 km)
1 hour ago