I think it would be really awesome if there was a companion app for FFXIV where we could join the seventh dawn members in some classic turn based RPG action to uncover the dark secrets of the ascians or some other side adventure. It would be a great opportunity for some character building and to tell an interesting side story. In addition, it could let players access the auction house, gather, craft, and even help with the gardening around the FC house. Perhaps items gained by playing the mobile app could be used by your character in FFXIV and vise versa.

Which would make it almost a complete game in and of itself, but it would be a great way to expand on the FFXIV universe and add a new dimension to the MMO side of things.