Look at this lovely video here.
The guy who made the video wasn't incredibly clear as to where the stone was exactly, but head to Santalune City, go to Route 3 (Ouvert Way, the route before it) and you'll find a pool of water. Surf over that and your beloved Dawn Stone will lay there before, untouched as any other item randomly lying on the floor that no one gives the thought of picking up. :3
Hope I helped. :)
Source: If you want to know what my source is you don't deserve to know. :3