Okay, I am super casual. I never had much interest in raiding and I also dislike Dawntrail so not really doing any progression at all this expansion. I still do old content though. Mainly play WAR. I respect and love to watch other players do the hardest content though!
Zones like Eureka and Bozja are fun, Frontlines PVP is really fun for me so I wish they had better game modes on the large-scale side of things and more maps. So pretty much "zones" that allow me to just hop in and grind with other players are fun in my opinion, allowing me to AFK whenever I need too and not waste other peoples time. If they could somehow simulate a giant on-going warzone that mixed PVE and PVP together I'd have a blast, and add in gear somehow that'd be great. And to clarify it doesn't have to be 100% PVP... think a circle of PVE and in the center is a bit of PVP would be fine also.
Personally I hope FFXIV goes back to their roots of how ARR was and focus more on the alliances and their lore as well. Let Limsa Lominsa have pirating back on the menu, and Ul'dah being cutthroat traders... and Gridania crying about whatever, heh. Introduce new factions to join besides the big three would be awesome as well like Ishgaard, Garlemald, Ala Mhigo, etc. And then let these factions go into conflict with each other! There is much they can do but they seem so focused on the Scions and saving the world plots. Lore needs to become a a lot more grounded and everything might just follow suit naturally in my opinion, a least in terms of the developers creating new ideas and designs for gameplay.
This is off-topic, but I'd also really like if they continued the stories of the initial classes we choose to become something of a "pure" class. What would happen if our characters continued being a pugilist or marauder, etc and never used the soul crystal? Could add a bunch of new skills and flare to these classes by the time they're max level.