One of the day trips you can do from San Francisco is to Angel Island, a thirty minute boat ride that passes Alcatraz (the inescapable prison, now closed).
Once there, I walked up Mount Livermore – a pleasant two hour circular climb, ascending about 240m. From the top, you get good views of the San Francisco skyline and Golden Gate Bridge as well as the bay area generally.
You can also do a cycle ride (or walk) around the island. I was too late to hire a cycle after my hike. They stopped hiring at 2.30pm, which seemed early in the day but is probably a reflection of people taking the bikes late and not returning for the last ferry at 4.30pm.