Hi Lynda
I've been to Alcatraz when I've been in San Francisco fairly recently (nothing to do with JY), and it can get pretty booked up.
If you want to go on a particular time, then I would suggest you book in advance, as it will be highly likely that if you leave it very close to the date, you'll find there is no availabilty
Enjoy San Francisco, it's one of my favourite cities.
Stuart