Final Fantasy IV/To The Moon

Fly to Mysidia
Once in the overworld fly immediately to your right and you will reach Mysidia. Enter the town, and the elder will greet you and raise the Big Whale for you. This ship will allow you to travel to the moon. Get inside and touch the crystal in the middle and it will take you to the moon.

Locate the Cave
There is a plateau that has a ramp downward and will let you enter the set of caves. It is to the upper right of the strange blue crystal towers. Land somewhere on the plateau, and enter the cave below.