SF is a unique and amazing town. Keep in mind one thing that's little-understood outside of California: San Francisco is not the same thing as the Bay Area. And when you say "San Francisco" you probably really mean the Bay Area. "The valley", proper, is around San Jose and the lower peninsula, for instance.
You should explore SF first, though. It's more condensed, and easier to understand on a short trip.
And thanks everyone for the help, I'm much more optimistic knowing that the community is this this helpful and supportive. Now just to cram it all into 3 days...
One more FYI: people from San Francisco rarely, if ever, refer to it as anything else but San Francisco, at least when spoken. E.g. they would not say "SF" out loud, and will never, ever, say "San Fran."
You should explore SF first, though. It's more condensed, and easier to understand on a short trip.