I write primarily at coffee shops.
My studio is awesome for what it is, which is a place to paint. It's all set up for painting, both digital and physical. And when the time comes to illustrate the books (I do hybrid comic/chapter books) I will spend four or five hours a day plunked at the desk illustrating.
For writing, though, I need exactly the opposite of what I need when I'm painting. I want to get as far away from the studio as possible, both physically and mentally, not constantly getting up, poking something, wondering if the paint is dry, staring out the window at the bird feeder, etc.
So I go to the coffee shop. My local baristas all know me, get me the usual, and then leave me alone. I have my table in the corner, I sit down, I hammer out my thousand words without checking my e-mail and fidgeting and wandering around, and then I close up the laptop and go home. It takes half the time it would in my studio.
(Much as I love the current place, I do miss my old stomping ground, which was a hole-in-the-wall cafe where I could get a chicken salad sandwich, a bottomless cup of a coffee, and a dill pickle to make strong men weep. Alas, they closed, and now I must forage for lunch on my own.)
It wouldn't occur to me to go so that People Know I Am A Serious Writer. I live in a small town, everybody already knows what I do for a living...