If there is only one central place to submit applications, then it is clear what to do.
So, we will presume that there are multiple email addresses, web forms, whatever.
You _could_ submit to all three, but things might get messy if all express interest.
My advice – if there is a a way to submit a converting letter, would be to make a single application. If there is no way to attach a covering letter, perhaps an additional front page to your CCV would suffice to pass a message. I have resorted to that before, and gotten the job.
Which leaves the choice of where to submit it. Perhaps to the head office? The one nearest to you? Your first choice? Only you can really decide that, although I personally would go for first choice.
I would explain that I am interested in multiple locations, and would express an order of preference, with reasons why. Hint: make these reasons that appeal to the company, rather than just saying “that one offers most salary” ;-) Interests in a project or its technology might be a good reason. A location close to family, which would tie you to the area might appeal to them. You get the picture, think of your own.