The best place to spend a rainy day reading in San Francisco is the UCSF Kalmanovitz Library on Parnassus.
The library is open to the public. You want the Lange Room at the back of the fifth floor. The Lange Room has half a dozen or so comfortable leather chairs, and large windows looking north across Golden Gate Park and the Presidio to the spires of the Golden Gate Bridge. If it was clear, you’d see the Marin Headlands, but if it was clear you’d be reading outside. The room is almost always empty.
It provides all the ingredients necessary for taking full advantage of a rainy day: a comfortable chair, plentiful natural light, good views, a book, and an environment that discourages human interaction.