While there are references to the mayor's annual report, reviewing the year past and setting goals for the year coming up, no one seems to call it a State of the City speech...or even pay much heed to it, for that matter. However, the City Charter (adopted in 1925) did require the mayor to report on the "condition and affairs of the City" to the City Council, before presenting the budget to the council. Lots of leeway there--the report didn't have to be given in person.
Mayor Sam Yorty used the term in 1963 to refer to four talks he gave in January, in four different parts of the city. By 1965, Yorty's State of the City talks were being televised on NBC.
This picture shows two of our illustrious past mayors--the not-yet-elected Sam Yorty, attempting to shake hands with Mayor Norris Poulson, who reportedly said "Not interested!" as he turned away. The man on the right is Poulson's lawyer. The date was May 11, 1961, and the occasion was a court hearing. Yorty, ever the scamp, had filed a $2.2 million dollar lawsuit against Poulson, charging slander--which, understandably, could put a damper on conversation.