If someone were to take me on a date in-game, the Gold Saucer immediately comes to mind, as does the sight seeing log. I would want to take lots of screen shots of us emote syncing and us on our chocobos. I would even love it if I was gifted with carnations and pearl chocolates.

I wish SE could implement something like this. Some kind of npc at the gold saucer that initiated activities you can do together with event related emotes such as holding hands, chocobos interacting with each other, and even small 3-4 second cutscenes of the joyful couple. I think it would encourage more interactions between players, which is really what mmos need.