Just because there’s a bay doesn’t mean that the term “Bay Area” is in active use. Whether or not it is seems to me the point of the OP.
Nah, it means Department of Motor Vehicles…Wait, that’s the MVA–Crap in a hat! 
Me three.
I keeps getting bigger. I think it’s common now to think of the 9 counties in and around SF to be “the Bay Area”:
Santa Clara
San Mateo
SF
Alameda
Contra Costa
Marin
Napa
Sonoma
Solano
Going from Memory, I think that covers about 8M people. A little bigger than Denmark; a little smaller than Sweden.
Massachusetts is still The Bay State. 
I’ve been to/through both the Tampa and Chesapeake area and bays, and have nothing against them.
But if someone asks about “the Bay area,” it indelibly sticks in my mind as SF.
ZZZZZACTLY.
True enough, but many visitors and residents don’t realize that just a few miles to the west and paralleling US-101 is I-280, and most of the distance between San Francisco to San Jose is rolling hills and wide open spaces. It’s a beautiful drive, and I avoid 101 as much as possible.
Same here. And I’ve been to and through Creve Coeur too, where you’ve got some rivers, and BIG ONES too!
SF first followed quickly after by Saginaw.
AND substantially less traffic! It would appear that even the residents of the area aren’t all that widely aware of I-280. How is that even possible?
There is (or was?) even a large billboard alongside I-280 proclaiming it the “World’s Most Beautiful Freeway” – Full of this sort of scenery.
LOI take 101 if it means that I can skip 5.
Sometimes includes all or parts of: Santa Cruz, San Joaquin, and San Benito counties. I don’t think of those counties by name often, but I’d be pressed to discount Stockton, even if it’s not a place I visit very often. It’s a local freeway terminus so I’ve always considered it local to the area. Same with Santa Cruz and maybe whatever towns are in San Benito.
ETA: looked it up. Hollister is like Charming from Sons of Anarchy and also San Juan Bautista. Both I consider closeish of the Bay Area but not part of it.
I used to live in California and Stockton was always considered part of the Central Valley (in particular, the San Joaquin Valley) and definitely not part of the Bay Area. You cannot classify anything east of Altamont Pass (or Fairfield if you’re going up I-80) as part of the Bay Area. Otherwise, they’ll eventually start including everything from Reno westward.
I thinks folks in Santa Cruz like to distance themselves from The Bay Area. It really is quite different “over the hill”. And heading north, there’s basically nothing between SC and Half Moon Bay except tiny Davenport. I think you can make a better case for San Juan Bautista than Santa Cruz.
I’m in the midwest but Bay Area always means San Fran and environs to me.
Yep. And I’m not sure I’ve ever heard of anything else called “the Bay Area.”
I posed this question to some of my American co-workers and while the vast majority answered correctly ( San Francisco ) one of them from Texas said that there is a “Bay Area” in Houston. After looking at a map there is indeed a sizable bay there.
I would have to say my brother’s back yard…he has three mature (and very vocal) Basset Hounds…
In truth, SF and enviorns whenever I hear “Bay Area”, unless I know that they are talking about the East coast, where my default is Chesepeake Bay.
I live in the Tampa Bay area and still don’t think of it as “the Bay area”. The real Bay area is where I was born, the Tampa Bay area is where I live and currently consider home. FWIW, I’m not sure that I’ve ever heard anyone here refer to this as the Bay area.
:)Best answer so far.
I live in Northern Virginia, so not that far from the Chesapeake Bay, but I’ve never heard The Bay Area refer to anything but the San Francisco Bay. We might say The Bay here, but never The Bay Area. I think part of that is that, at least as I understand, the San Francisco Bay is much more homogeneous than the Chesapeake is, and the latter is also a lot larger. There’s parts of this area that are very urban, parts that are very rural, and really, it just doesn’t make much sense to lump, say, Baltimore, Norfolk, and the Eastern shore all together. They’ve far less in common than San Francisco and Oakland.
And I’ve spent the most recent 17 years of my life residing within a mile of the Chesapeake Bay. Same deal: unless I see the phrase ‘Bay area’ in a very local publication (e.g. the local free weekly, which is called the Bay Weekly), I’m thinking San Francisco Bay.
When talking to people from other areas, I often say “San Francisco Bay Area” to avoid confusion. I think I’ll stop doing that now.
BTW, technically San Francisco Bay isn’t really a bay - it’s an estuary formed by the Sacramento and San Joaquin Rivers.