Thanks, everyone! You've provided lots of good information!
My favorite answer was the handy "Find Nearby" link on Yahoo Maps. I wonder when Google Maps will copy them.
While reading the reviews of a reasonable hotel near the Oakland downtown BART station, I came across someone's recent report of being mugged just a block away from the hotel, in the daytime.
So, I've taken Mrs. Middle_Seat's advice to stay in San Francisco, and will spend my last free night award at the Embarcadero Hyatt.
And I will be there on a Tuesday/Wednesday, so do not need to worry about the weekend BART schedules.