The nearest one is 5 hrs south, near Morro Bay: Diablo Canyon. It's being shut down soon. There was a nearer one at Rancho Seco but it was shut down. There's another one in SoCal at San Onofre but that one is shut down too.
Oh and I remember that Berkeley is a "Nuclear-free Zone" (you'll see the signs as you enter) but that they once had a research reactor :D
Two not so far away, but it would take an incident worse than Chernobyl to create long term issues for the bay area (one could perhaps debate the threshold of what a long term issue might be)
