I would say: "the rumor spread up the West Coast from LA to San Francisco," but that may just be a stylistic preference.Can the opposite be said, like "the rumor spread from LA to San Francisco, up the West Coast."?
There is an odd twist to this discussion. On the east coast of the USA, in New England in the 1750's 'down' meant North. The term referred to the direction that the wind was blowing. Boston to Canada was down wind and sailing down the East coast meant sailing North.
I have always understood "down east" to mean Maine, from the point of view of the rest of New England.
Thank you everybody
I'm sorry, I should have quoted a little longer from the text. I quoted it from an elementary school history textbook of the US. I borrowed it from my nearby library, and have already returned it. It belongs to another city library and had been sent to my nearby library. If I borrow it again, it is going to take some time to reach me. As it is a school textbook for US children, I think the "down" is an ordinary meaning; that excludes the meaning "toward Maine," right?
That leaves us the rest three meanings:
(1) along (as andrew said it),
(2) a large proportion of the east coast, more distance than just "along (badgrammar),
(3) from north to south (Old Novice and others)
I enjoyed your explanations and comments so far, but I have a feeling it's going to be even more interesting discussion.