I don't care what anyone says, I would play the crap out of a Noctis Window Cleaning Service minigame. xD Nice one, black orb.

Other than that, just fun things like chocobo racing, card games, monster collecting/growing/fighting (Final Pokémon Fantasy), lots of platforming-related stuff because of his ability to teleport. I hope that there will be decent reward for exploration, too, and some optional dungeons that are off the beaten path. Wouldn't object to a FPS minigame either, since there have been FPS elements shown off beforehand (I think?). Would be cool to suddenly see the world in first person whenever you want to.

Imagine free-running through a city as Noctis, teleporting here and there, in first person (Mirror's Edge style, but with teleporting). That would be awesome.