Recreation in Eorzea?

[WhiteArchmage]

We do know thanks to events that the Mi'Khetto's Amphitheater is used... as an event venue. Not just in timed events but also on job quests (especifically LTW), it's used for showcases, official GC events, and assorted theater and entertainment stuff. The Rising and Little Ladies' also put up stages in the Ruby Road Exchange, so we can infer that similar troupes (like the Songbirds) perform around there from time to time (plus the eternally dancing girls next to the Quicksand).

Not in Eorzea itself but the Majestic Theater Troupe also tells us there are OTHER theater troupes around, and Kugane has both the geiko and kabuki performances.

[RobynDaBank]

Mahjong needs more reach!

[DentiusChestus]

You could always hit the pluto and somnus (don't.) I'm sure every region has a fairly diverse drinking culture. In real life, before things like prohibition and the industrialization of agriculture, most households brewed what was on hand. Drinking was probably more fun and varied.
Not to mention the widespread availability of moko grass! The crafting vendors sell it for an unbelievable 2 gil a stalk. Guess the city states haven't levied the recreational tax yet.

I'm sure there's a thread on drugs and recreational substances in the forum somewhere. They seem to have removed most references to smoking and such in the game, aside from the occasional drink and Tsuyu's pipe, most likely due to ESRB and PEGI concerns. Hilariously, the one pugilist quest where someone uses pluto to get a defense buff is STILL in the PEGI notes for FFXIV, even the Endwalker expansion specific ones. It's funny how you can tell whoever audited ARR way back started as a pugilist and caught that, and it just stayed in someone's .CSV file for every future installment.

If you want to use your imagination, I'm sure the guilds could give some insight onto what entertainment is available. Professional woodworkers and goldsmiths would be good candidates for making figurines, game boards and pieces, and puzzleboxes. There's that little playground in the Gridania woodworkers' yard. Simple bar diversions like darts and team games could also be viable.

Anyway... Seems most of the other canon diversions I could think of were already mentioned. Unless you want to come visit the Hrothgar bathhouse.

[Brightamethyst]

The Monster Toss arcade machines imply the existence of basketball.

[Hycinthus]

Is there no worldwide accepted sport like Blitzball in FFX or Quidditch in HP? I think there should be. Maybe in next expansion.

[SannaR]

Sport? No. The only thing that everyone seems to play or at least has reached to all corners of the star and then some is Triple Triad.