I have this small room in my house with a chair, a desk and a desktop computer.
Meh... I don't like being in an empty room with a computer. I like having my television on in the background for some sound. Feels awkward when I'm in my room and it's all quiet while I'm typing.
I almost always log in on my home laptop (family laptop :/ ). However, sometimes I go to friends' houses, and then other people come over and they go play Call of Duty, which I hate, so I will log in at their houses occasionally, too. :P
I've never logged in at school, but I have done Minecraft there! :P
Well this question is a little dumb, the only place you really can play it is at your house. I know sometimes you go to a LAN house or a library or your friend's house to play it but the main place will always be your house.