While the word "jazz" actual origins are unclear, a reporter from the San Francisco Bulletin, "Scoop" Gleeson, utilized it repeatedly in his articles as a descriptive baseball word for his stories about the San Francisco Seals beginning on March 6, 1913 while at the training camp in Boyes Hot Springs. "Jazz" as a term for the music genre may very well have originated in San Francisco.
Art Hickman and his band were hired to provide the entertainment at the Seals training camp and because of that gig, they were also hired at the St Francis Hotel when training was over. When Art Hickman died in 1930, his obituary stated:
"The man who took the tom-tom throbs of San Francisco’s old Barbary Coast negro rhythms, adapted them to the wail of the saxophone and twang of the banjo and gave the world its first jazz music, died yesterday afternoon at the St. Francis Hospital." (this is a direct quote, not meant to be offensive)
One fact I do know is the term "jazz" in describing an African-American form of music was considered to be somewhat of an insulting or derogatory "label" from the old-time musicians such as, Louis Armstrong, et al. But after Art Hickman's death, the musicians in his band relocated to other parts of the country and described the type of music they played as jazz. Whether or not this had anything to do with the acceptance of the term, I do not know, but I do believe that the word "jazz" has deep roots in The City regardless. Here is some interesting reading for you: