"Worth" is a totally personal and subjective value. We don't know you, so how can we decide "worth" to you?
You can see the Golden Gate sailing in and/or out, so that could be a low priority.
"Going to an island"? That would be Alcatraz, the famous prison. A very popular and interesting destination.
Muir Woods is neat and unique. Sounds like it may require a private tour in your case. It is VERY high demand to see Muir Woods, and reservations are required, which your tour would take care of.
Weather will not be a factor at Muir Woods, or at Alcatraz, really. Only sailing under the Bridge. It can be clear, or foggy. Won't know until a day or two before.