During Disc 1, you will go to the Gold Saucer twice; during the second visit, an event will happen where a member of your party will come to your room and invite you out to some parts of the Gold Saucer.
Depending on choices made during specific events in the main game, the character that comes to see you will change.
Below are the mechanics and the choices that make changes. You can be visited by: Aeris, Tifa, Yuffie or Barret.