In the Bay
Here's another great tiny island. East Brother lighthouse is located on an island by the same name in San Francisco Bay. And by tiny, I mean tiny. The island is less than an acre in size, accompanied in this stretch of water (the San Pablo Strait) by an even smaller island called West Brother.
West Brother is barren and inhabited only by seagulls, but, as you can tell from the pictures, East Brother is occupied. Potentially by you, if you'd like to stay the night in its Victorian B&B. The whole set-up dates back to the 1870s, with the lighthouse active for over 133 years and the house converted to an Inn 26 years ago.
Though it appears to be totally isolated (and may even be a little spooky at night), it's only a ten-minute boat ride from the city. So you can bask in glorious isolation and do nothing but read a book for a week, or dip in and out of the city. Scooby-Doo, where are you? RM