There's also beast tribes. Each expansion has 3 beast tribes (ARR has 5 instead, but they take less time to individually complete) that serve as daily quests. Maxing out each beast tribe in an expansion unlocks a questline that gets you extra goodies (on top of the mounts, minions, emotes, etc that each beast tribe gives individually), but you'll need a crafter and gatherer leveled on top of a combat class to access them all (in HW you just needed a crafter for one tribe, in SB you could use either a crafter or gatherer for one tribe, in ShB there's a tribe for combat, crafters, and gatherers each instead of 2 combat tribes and one tribe that was crafting or crafting and gathering.) It takes roughly a month to max out any given tribe, and you can be working on two to 3 per day (the numbers are a bit different with ARR due to how they work).

Short version, for current content look into the Eden Raids, the Nier Alliance Raids, Bozja (for the relic weapon, first do the Return to Ivalice Alliance raids), and the Sorrows of Werlyt for the Trials.
The Eden Raid's final tier will be out in December (likely) with 5.4, the final Nier raid tier will be out like 3-4 months after that, Bozja will likely get another phase in 5.4, and Sorrows of Werlyt will get a new fight in both 5.4 and 5.5. (And the combined beast tribe quest will likely be in 5.55, the final final main patch before 6.0).