It seems like pretty basic functionality and I think I must be missing something, but is there a way to move documents within the skydrive web app? It seems like this feature was lost in the recent overhaul of Skydrive.
Mark the little checkbox in the upper right-hand corner of the tile that represents the document in your SkyDrive.
Click on Manage in the bar on the top, then click on Move to.
You'll now be given the option to select the target location for your file.
Alternatively, SkyDrive also supports Drag & Drop to achieve move operations: