What is the first region that comes to your mind when you read or hear the term “Bay Area”?
San Fransisco.
SF: then again, living in the Northwest your chances of hearing of the other areas is almost nil.
I spent the first 16 years of my life living near or in the DelMarVa penninsula. “The Bay Area” makes me think of San Francisco.
San Francisco
SF Bay Area. But of course I live there, so…
I live only 50 miles from Chesapeake Bay and have gone sailing on it, but San Francisco Bay is what comes immediately to mind; in fact, that’s the only one that comes to mind. Around here, we may refer to Chesapeake as “the Bay,” but there’s no phrase “the Bay Area” applied to here. Instead we call various parts of it the Washington-Baltimore area, the Eastern Shore, the Northern Neck, etc. I don’t think there’s any single name for the whole circum-Chesapeake region. It’s too large for that and it comprises a number of regions.
My sister lives in Oakland, but that didn’t bias me at all either.
My answer too.
When I was stationed at Long Beach, the folks down there called it the South Bay, and being from San Francisco that sounded a little odd. To me, South Bay means San Jose and the surrounding area.
But, a bay is a bay is a bay, so bay area can be pretty generic.
But, Bay Area? There is only one! 
And we’re currently the baseball and basketball champions. The New Title Town. So take that, Green Bay and Pittsburgh!
I was born in Berkeley, and grew up in Orinda and Oakland.
I’ve never lived anywhere close to SF, but that’s where the Bay Area is.
Even though now I know they’re talking about San Francisco, that was only clear to me so very recently that I will give my genuine answer if you’d asked me two years ago: I didn’t have a clue what they were talking about at all. It was just some anonymous zone of America that I was unfamiliar with.
Even now there are a couple of other areas/references where that’s still true, but slowly I piece those kinds of things together as context clarifies. e.g. I know a lot of people aren’t certain what “New England” refers to, or what the Florida Keys are, or the Mason Dixon line, or the Bible Belt, or what Upstate New York means, or where the Tri-State Area is*. I know (vaguely) what those are now, but it’s not easy to figure out things like that most of the time.
*turns out, it’s everywhere and nowhere
In a national context I’d assume the SF area was being discussed.
But Galveston Bay isn’t far from here. There’s even a Bay Area Boulevard linking neighborhoods near NASA.
Even just in the USA, there are lots of bays.
I think of Hawkes Bay Karachi, near which I lived at one time.
While it is the SF area, I don’t know what area of and around SF it refers to. The city and the surrounding areas that touch the Bay, including Oakland? or a much more limited area similar to how Manhattan is divided into sub area such as SoHo,Tribeca, Upper East/West Side, etc. I assume it is a larger area just because it is such a popular term, so many people seem to reference it plus I don’t recall any other subdivision for SF used. So more like a term used for the NYC metro area which goes well into NJ and CT (and a good chunk outside the city limits in NY.)
Ohioan here. Yup, San Francisco and its environs.
San Francisco, but I never vote in public polls.
I;ve lived in both Berkeley and St. Pete, but for whatever reason Tampa is the first one that jumps to mind when I hear “Bay Area”.
(Isn’t the Boston area sometimes called the “bay area” as well, or did I make that up?)
I’ve had an online conversation like the following:
Me: Where are you from?
Them: The South Bay.
Me: California? I’m from the East Bay.
Them: Cool!
(Lots of conversation later)
Me: Err… you’re not from anywhere near San Jose, are you?
It was either LA or San Diego, but that doesn’t scan with me.
A window where the dog or cat sits.
Same here.
Except for the sister part.