Once you gain control of the airship after the events in Zanarkand, you can unlock a number of areas in two ways: manually searching the map for the X/Y positions of the areas, and others via passwords. Here, I will cover most of these areas, though only the minor areas are covered in the scope of this particular section - see the links for the larger areas.
Password (CASE-SENSITIVE) Area Unlocked Details:
GODHAND - Mushroom Rock - Go north to find Rikku’s Celestial Weapon, the Godhand.
MURASAME - Besaid Ruins 2 - Open the chest nearby for Auron’s Murasama katana.
VICTORIOUS - Besaid Ruins 1 - Go around the structure to find Rikku’s Victorious armor.
(X,Y) POSITION COORDINATES (approximate)
X Y Area Unlocked Details:
12~14 58~61 Baaj Temple - See Baaj Temple for more.
40~42 57~59 Battle Site - Easily grab the Phantom Bangle for Lulu here. It has Fire/Ice/Water Eater.
30~32 73~76 Besaid Falls - Easily grab the Dragoon Lance for Kimahri here. It has Magic Counter and Evade & Counter.
34~36 56~58 Mi’ihen Ruins - Easily grab the Sonar here, which has Initiative and Poisonstrike.
71~73 35~36 Omega Ruins - See The Omega Ruins for more.
13~15 42~44 Sanubia Sands - Easily grab the Ascalon for Tidus here. It has Double AP!