I'd say that my favorite sort of side story is either The Snake or Nimander/Twilight/Shore
Edit: Basically the entire Tiste Andii subplot from the meeting of Clip with Nimander and Co, to the battle at the shore.
I'm just getting back into ffxiv. Stopped playing a couple years ago cause my brothers quit on me, but now we're back. Still have to finish ARR though, so I've got a ways to go in catching up. Made a new character for coming back.
@Ammanas and I read it together on release last year. I think it had a decent ending to the first story and then a good set up for where it's going in the series. But I'm also a horrible critic, lol, so I'll let him weigh in too.