Move function for a game
I would abstract the animation logic into a high order function and the possible directions in an object, then just lookup the corresponding function for each direction, in other words:

function move(to, dir) {

  function animate(props) {
    return function() {
      $('#player').animate(props, 'slow', function() {
        $(this).attr('style', '').appendTo('#'+ to);
      });
    }
  }

  var dirs = {
    right: animate({ left: '+='+ scale }),
    left: animate({ left: '-='+ scale }),
    up: animate({ top: '-='+ (9*scale/10) }),
    down: animate({ top: '+=' + (9*scale/10) })
  };

  if (dir in dirs) dirs[dir]();
}


I fixed a few other things. You can use $(this) to refer to the element being animated in the callback and chain those methods.

Then (9*(scale/10)) is effectively the same as 9*scale/10; associative operators.

You probably need to abstract even more if you add more code; ideally you'd want separate all your logic from your DOM manipulation and create a clear data structure that you can reuse. Also think about using classes instead of IDs. Classes are more reusable and lead to simpler code.