You may find parking difficult at Muir Woods at 10AM, even on a weekday. The lots are small and people park on the side of the road for a couple of miles on either side of the entrance. I realize that September is post Labor Day but right now the freeway signs on Highway 101 are on by 11AM that Muir Woods parking is full.
Muir Woods does not require 4 hours unless you plan on doing extensive hiking out of the Woods. Which is possible as various trails are accessible from the Woods. But to just wander through Muir Woods itself is easily done in an hour. Or perhaps a bit more.
Additionally, Sausalito is a small (rather touristy) town. I can't imagine spending more than 90 minutes strolling the shops.
The title of your thread suggests you want to into SF and go to Alcatraz as well. Is that part of the plan? There are plenty of day tour tickets available for Alcatraz (night tour is sold out) for September but I wouldn't leave it for long -- it's pretty well completely sold out through August 23.
Start your own thread in the SF forum. The Marin County forums don't get much traffic. Tell us when you will be visiting, what day of the week you want to go to Muir and anything else about your travel party. (I don't know what you mean by "SF bay")
Muir via public transit is only available summer weekends.
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