Listed in Hibler-Kappen's "So-Called Dollars" book, 1963. There are several contemporary pieces commemorating the 1906 earthquake that are companions to this piece. Similar size and die-work. The question is why the Cliff House and Post Office? Jerry S has figured this out. He suggest that these two buildings were among the most significant survivors of the fire hence celebrated on this souvenir. If this is true, the piece pretty much has too be a 1906 issue.
Info courtesy Michael Wehner

Token used in an orchestrian at the Cliff House. They used to have either the actual machine or a similar one at the Musee Mechanique. Basically a player piano with a bunch of other mechanized instruments inside it. The token is small, about 16mm.
 Scan & info courtesy Michael Wehner

"I was giving a talk about Sutro’s yesterday and an elderly lady gave me the attached “Sutro Baths” token. She said her parents had gotten it around 1912. I have no idea what this was little token was for. It’s made of brass, has black enamel finish, and measures 1” in diameter. The front says Sutro Baths, the reverse is blank. It’s not a locker room token because there’s no number anywhere. It’s probably not script since there’s no value indicated."
 Courtesy John Martini