Hmm, I don't know why you're getting these answers, seems a simple question with a simple answer. (unless I am somehow misunderstanding, of course)
So you make your selection, using Magic Wand or any other selection tool. Then simply click inside the selected area & drag - the selection will move, not the pixels. Just make sure not to change to a 'non-selection' tool (e.g., the Move tool) before you drag.
If you take the Save to an Alpha Channel route, that will work except for the fact that when you move the channel/selection around, you will find that some additional areas of your image become selected. You'll have to go into Quick Mask mode to paint them out in order to get just the selected area you want...
HTH,
John