Putah Creek is the closest fly-fishing option to San Fran. It's about 1.5 hour drive (be careful coming back into the city at rush hour - tons of traffic). It's a neat tailwater with lots of good pockets to fish. Can be tough. I fished it back in December and caught a few on egg patterns. I don't think they're spawning right now, but be careful if they are. Hire a guide if you can - its not easy water.
About a 3-hour drive north is the town of Redding. Gateway to the McCloud, Pit, and Lower Sacramento. The lower sac is a great float trip. Call the Fly Shop in Redding and they'll set you up.
Water levels in CA right now are super low - keep that in mind.