Coil 2 or 3, because its still my favorite side story in the game, AND the feeling of having to earn the right to view the next segment felt so accomplishing.

In terms of fight, Midas, but everything else, I'd say Coil because I love the idea of adventuring deeper and deeper into the Eorzea with the map giving details on how deep you were, I loved seeing the Dalamud from the inside, fighting Twintania on top of Bahamut's hand etc. Least favorite would probably be Gordias, the boss design wasn't really that great, Alexander is cool, but the story was forgettable at that point, and mechanically, it was just there and not really fun. Midas was a much better balance of difficulty and fun mechanics.