Final Fantasy III/The Airship Nautilus

Let's summarize the equipment you found for free in the last few quests:
 * Full equipment for Dragoon (two different spellcasting spears, armor, helm);
 * Full equipment for Viking (spellcasting hammer, armor, helm);
 * Full equipment for Geomancer (status-inflicting bell, armor, bracers);
 * More arrows for the Ranger.

The next dungeon is miniaturized, so physical attacks will be useless. Not only that, status-inflicting weapons (Earth bell, Medusa arrows) are uneffective, too. You definitely need as much magic as you can.

Keep one Dragoon for his spellcasting Wind Spear, keep the Scholar (DS) or the Ranger (NES) for healing, get the Geomancer for his Terrain ability. Finally, head to Replito and purchase the five summon spells for the Evoker: even the Chocobo Escape will be useful in a miniaturized dungeon. For the rest, the Evoker equips the same rods and armor parts as the Black Mage.

Cave of the Magic Circle
A miniaturized dungeon. Enter, explore one floor to find the shortest route through it, then exit, rest and re-enter to explore deeper. Some enemies are weak against Wind, so the Dragoon's wind spear will be useful. Luckily, there is no boss at the end. The Magic Circle at the end allows to enchant the airship Nautilus for underwater travel.

Dorga's village
Optional area. You can buy Level 7 magic spells here. Access from underwater on the east side of Dorga's continent.

Temple of Time
Underwater dungeon. It conceals the Magic Lute necessary to wake up Unei. There are many locked doors and also the strongest knife for the Thief, so you may consider temporarily switching one character to this class. There's no boss at the end.

Underwater Cave
Optional dungeon. It contains several useful pieces of equipment.

Saronia Catacombs
Optional underwater dungeon. Defeat the boss, Odin, to obtain a Summon spell.