Sacramento, San Joachim, Tuolumne, American, Napa, and Petaluma are the major rivers I can think of.
Sacramento you should be able to do from Redding, if you can handle some minor rapids.
Tuolumne is done annually by the Tulumne River Trust as part of their paddle to the sea program. You can check with them on where it gets flat enough for non whitewater craft (and maybe join their program). http://www.tuolumne.org/content/index.php?topic=programs
Not sure about how far up the San Joachim. Seems it should work from at least Fresno.
American would be from basically just east of Sacramento (unless you were willing to portage over the dams)
Napa is paddleable from just above the town of Napa.
Petaluma from Petaluma.
You could always start in the South Bay and paddle across the Bay itself.