Aw man. I always love questions like this! Cx I'm boring though, so whatever.
Whenever I think of making a character, it's like I've been trying to remember someone I knew a long time ago. I try to think of things they would do, or foods they like, or of memories I have from somewhere. Or, if I like a character from some story, but one aspect of theirs bothers me, I always tweak it, and then apply that personality to some other character I've thought of somewhere. Most of the time, though, I just decide to throw things in the mixing pot, and then pick out everything I don't like. That's really all I do, anyways...
Anywhere, everywhere. Imagination, anime, real life, other books...list goes on and on.
For my most recent story, the idea itself started with my main character. I was getting back into drawing and she popped onto the paper randomly. Whenever I tried to draw another person, she was there. I tried to draw items (ice cream, umbrella, bridge, etc) but she still came out of my head and onto paper (eating the ice cream, using the umbrella, dancing on a bridge, etc). So I soon got curious about who she was. Over a week I learned more about her and eventually, her name. She introduced me to two more characters while I introduced her to two of mine. And thus a story started to form.
Since I have many contradicting aspects to my personality, it's very easy to base characters on myself and still make them different from each other. Generally speaking I tailor them to situations where I think they can work best.