Randy Murray raised a few interesting points (some time ago - this has been sat in my Pocket queue), I think that the primary reason why a cafe or coffee shop is a popular destination is that it provides a crowd that you are alone in. When you're around familiar people, friends and acquaintances - even if they're not distracting you directly, you have a tendency to pay them attention. The people in a coffee shop are strangers that most of us by nature avoid paying too much uninvited attention to. Their passing us by fades into the bland noise of the setting which you don't even notice after a short while.
Sometimes 'quiet' is a state of mind, more than a physical reality.