There are different things that you can do to pass time after story.
You can:
1) unlock the normal raids . then if you want some content with a bit more meat go do savage after you do the normals. there are also ultimate fights for an even meatier challenge if you go through with savage
2) you can unlock extreme version of trials you did prior , they are a decent start
3) you can level other jobs from the very start though it isnt what id call an endgame
4) you can try your hands on crafting and/or gathering , its a game in off itself along with trying to get as much gil as possible. if gil is not your fancy you still get benefits from it, such as being able to self repair whenever you want, as well as being self sufficient on gear, food and pots
5)You can try your hand for bosja , i dont remember where the quest starts but by going for it you also unlock the relic quests. Relic is a weapon that is only outshined by the current raid weapon. In bosja you will find imo the best content in the game, a 48man with exclusive actions to use and a focus on Co operation between the parties that you have to make from scratch.
6) Glamour