True, San Francisco City Hall is indeed a public building, but to have a wedding there does indeed require a paid reservation and adherence to their documented process.
Below are a few helpful hints and links to information that isn't easily found on the San Francisco County Clerk-Recorder's website at first view:
Plan early - City Hall is a very popular venue for locals, but the competition for a wedding date extends to couples worldwide. Since there is no requirement to be a U.S. citizen to marry here, many couples from around the world plan their vacation here and a SF City Hall wedding too!
Personalized Wedding Ceremony - If you prefer a ceremony that reflects more of your cultural, spiritual or religious beliefs then you should hire an officiant to officiate your ceremony instead of utilizing City Hall staff. NOTE: You'll still want to reserve space for your ceremony when you apply for the license.
Guest limitations - You are limited to six guests (other than the couple marrying) and that includes your photographer and children too. More than six guests? There are a few affordable week-day options within City Hall that permit a larger number of guests: