I would think Seattle would be the city that would have that much rain and have that cool weather feel.
If it's a "Defending the US" approach - it could very well be Seattle.
Actually - I have no idea on this one... did BF3's Campaign (wait, what? lol) have a logical conclusion, or did there seem to be a cliff hanger?
To me, if the Ruskies are still the baddies, this time they are invading,
That one point in the image even resembles the Space Needle a little bit. It could just be just about anything, however.
And it could easily be any well built-up metropolis throughout Eastern Europe, Russia, China, even some Euro-Middle-Eastern regions like Turkey (particularly Istanbul or Ankara).
It'd be kind of neat to see the story take the "defend the homeland!" approach - more so for the multiplayer. But a wet, possibly chilly, and overall dreary metropolis scene is hardly a guarantee it has to be set in North America.