I laughed when this topic came up. I am definitely one of those writers who can't deal with distractions. Writing in public places is not going to yield much of a word count. I might get a whole fifteen words written. I'm too on edge, too alert to the happenings around me to sink into the brain space of creativity.
I much prefer to write in a cave, usually a dark cave where the blackout curtains are drawn, a lone lamp lends the barest hint of light, and no people are anywhere near. None. Nope. I'm a curmudgeonly vampire in that respect...okay, in many respects. Yes, the dog will force me into the light just long enough so he can pee, but then it's back to the oubliette where I am most productive.
That's right folks; when I have a hot date with my imaginary friends, it takes a lot of alone time to get them fit for public. Don't worry, it's not you. It's us.