Hi Peter,
I spent New Year's Eve in SF some years ago.
On arrival I asked the cabbie to take me to a motel, a good budget type.
One that was near a train station. Easy access "Downtown".
It was excellent. $70 US.
Alcatraz is almost a full day tour. Boat under the Golden Gate and then the island tour through the old jail cells. Get there early.
SF itself is like stepping into a movie scene. Particularly if you remember seeing the movie, "Bullitt" (Steve McQueen)
Enjoy your trip Peter
Cheers