It would be cheating to count story exploration so I will not count stuff like Yuffie, Vincent, making Aerith's flower cart and the Den of Woe. Stuff I mention can still contain slight story stuff but not that big. Searching for Friends also is way too much of a story-heavy sidequest. Those things should not even be optional. I also don't count saving the souls of your friends in Lightning Returns because it is required for the True Ending. Basically I could not even choose X-2 because of that but it kind of gives me a bit of wiggle room.

Ruby WEAPON & Emerald WEAPON
Final Fantasy VII-1
They will forever be MY ultimate gag secret bosses.

Pitioss Ruins
Final Fantasy XV
To be loved as much as to be hated, The only optional dungeon that is better than the Via Infinito for me.

Via Infinito
Final Fantasy X-2
Creepy atmosphere and a few interesting story pieces. I HATED how Floor 80 or 100 did not have Seymour and don't come at me with "but he was sent" because the dungeon is full of people who were sent like Yunalesca e.g.

Chocobo Breeding
Final Fantasy VII-1 & IX
Chocobo Catching, Racing, Hot & Cold, running around the world map and finding treasures and finding out more about Chocobos and their mysterious locations. Good stuff.

Underwater Research Laboratory
Final Fantasy VIII
I just love something like that. I already like those ruined technological and yet hidden places in the first places. But this one here is the very definition of it. Somewhere hidden at the end of the world map and it reaches down to some excavation place in the ocean where WEAPON sleeps. And it has Bahamut the Great Girlfriend.