I was born in SF and lived in the East Bay until I was 14 when my parents moved across country. I ended up staying on the East Coast. I am dating myself here.... I can vaguely remember as a small child when it was still open and recall the specific escape that made them decide to close it down. Inmates had tunneled through the concrete walls with teaspoons because the elements of the bay had deteriorated it so. I more clearly recall the Indian occupation of it and also when the last few holdouts were forcibly removed.
I have not gotten back to the bay area as often as I would like and have yet to tour Alcatraz. There is so much to see and do in that area but doing a tour of "The Rock" is definitely at the top of my list for the next visit.