I write on my computer at home, either with a playlist on, or the radio. I find it easier and calming, as long as no one is watching what I'm doing.
Sometimes I will write on another computer, like at school but they tend to be annoying which can break my flow of thoughts, like now the spacebar is a bit fucked and has to be pressed in the middle.
I actually find it really difficult to write on paper, but I do brainstorm on paper instead of revising for a pyschology exam when my parents banned me from my computer.
For mentally writing, anywhere, and I mean anywhere. Lessons, when I'm walking to and from school, car journeys, shower. I'll come up with an idea and keep replaying it, tweaking it until I get to a computer to type it up.