Ah, the St. Francis Riding Academy....I lived a block away on 6th Avenue, and every once and a while a horse would get loose and a group of horsemen (we thought they were cowboys!) came after the scared beast with ropes to bring it back to the stables. The building dated from 1904, as the San Francisco Riding Club. It lost the entire north wall (of the auditorium section) in the 1906 earthquake with bricks strewn all over C Street. I have lots of memories of hanging out around the Academy. It was torn down in early 1958, resulting in a major rat problem in the immediate neighborhood until for a few months. Safeway constructed a scaled-down version of the Marina Safeway on the site, opening in late 1959. That unit was torn down in 2007, followed by the current Safeway.
I have pictures and have done research, so hope to write a more complete history of the St. Francis Riding Academy for SF West History some day.