What is there to do once you hit 50?
It sort of never ends.
Once you hit 50 with a class:
-Complete your class quests (if you haven't already)
-Then proceed to your job quests(Lancer -> Dragoon, Conjurer -> White Mage, and so on) and get all of the AF gear.
-Will probably want to start on your relic quest for whatever job you are doing. This involves taking on all the major primals, Ifrit, Garuda, and Titan (along with Chimera and Hydra).
-Then start working on your Dark Light armor. This is pretty tedious but if you have any desire to progress to Coil and any of the extreme primal battles, this is a necessary step. I say step because you'll eventually upgrade that. You purchase dark light with the philosophy tomes you acquire from running dungeons (Amdapor Keep, Wanderer's Palace...), along with the primal battles as well. You can rack those up as fast as you can, but for the mythos tomes, there is a cap per week you can earn. Used to be 300, but now it's 450. You'll use these to purchase your relic materials and your AF2 gear.
-Also, it's a good idea to try to get a primal weapon on your way to relic. You'll get some from the dungeons but they don't compare. I never got any of Titan's weapons, but Garuda's was pretty legit prior to relic.
-Now there's a slew of other end game runs and whatnot that I haven't even touched yet. And it's going to keep going, I'm sure.
So yeah, there's plenty to do.