What is the place where you watch motion?

I'm not sure as to exactly what you mean by place, but the term for what your position from where motion is observed is called a frame of reference, or reference frame.

*Be sure that when working on problems that you know whether the frame is accelerated or non-accelerated. * This is because if you are observing a force from an accelerated reference frame, that force may be able to be explained by another force, such as 'centrifugal force'.