I know that all Playlists are listed under the Library tab. But I was wondering if they are saved somewhere else on the computer. For example, when I reformat the hard drive it was possible to open old Playlists as the where saved in “My Documents\My Music\My Playlists”.
That's the default location, unless you have changed it. To see where WMP is attempting to save the playlists, create one and save it by selecting Save Playlist As... from the drop-down button at the top of the playlist pane in Now Playing mode. In the save dialogue box that appears, hit the drop-down at th top to see where it is saving it.