1951, 1952, 1953, 1954, 1955, 1956, and 1957 all have the listing for the Strip location "Los Angeles Highway" and/or "3417 South 5th Street.

I don't seem to have a phone book for 1958 (I hate when I'm missing a potentially important date )

Alan showed the listing from June of 1959, which included the downtown location.

November of 1959 was back to listing only the Strip location...along with 1960, 1961, and 1962...and that's when I stopped looking.

The ad from June 1959 (which doesn't even mention the downtown location)