Also along with the classic creepy theme when you entered? Personally I think it would be neat just to have new hangout spot with more MGP games on the side to play around with. I remember when I first played that I was a little disappointed that Ghost Square didn't exist in this version of the Gold Saucer.
If not that Square, would you want any of the other squares get a cameo?
It would be interesting, but if it's going to be a functional inn, then it would possibly result in stability issues for the area as it would encourage players to idle there - unless it's instanced. Having said that, I can definitely see the decor as being something like Eorzea's actual haunted house Haukke Manor... although given the story of the place I think it would be in very bad taste if Godbert used that as the basis for a hypothetical Ghost Square. So, alas, I don't see it happening I'm afraid.
One thing from FFVII's GS that I would love to see here though in FFXIV is Battle Square - a 1-on-1 PvE arena with similar handicap reels giving bigger bonuses the longer you manage to last (although naturally balanced for FFXIV's battle system and classes/Job abilities), so simply going into it expecting to crush your way through with high ilvl gear wouldn't work, it's basically a battle of wits.
A final minigame I would also love to see in Gold Saucer (that doesn't have a FFVII counterpart) would be some kind of mount jousting (chocobo specifically), although I think Ishgard's Proving Grounds would perhaps be better suited to something like that. ;)
If too many idling people would be an issue (and/or to save remodelling the main area) they could always add “another floor” like the racing/Verminion area. Or an instanced one like the Triple Triad Battlehall might work for the Battle Square.
And funny you mention the Proving Grounds. I was just thinking the other day that nothing ever actually happened there. I wonder if it’s a future plot point?