(This information was all taken from WIkipedia).
Final Fantasy XIII
Two locations have been revealed to the public so far; Pulse and Cocoon. The world of Final Fantasy XIII is called Pulse. The overworld is plagued by monsters, though little else is known about it.
Cocoon was created by a Crystal as the ideal environment for humans to live in. It is a haven for humankind against Pulse. Cocoon is a beautiful city floating in the sky. It is defended by the Crystal which created it and many advanced technologies. The Crystal creates many things for the city and its inhabitants, such as machines for the people to use. It also produces living beings and raises them.
The people of Cocoon perceive everything outside of Cocoon (the world of Pulse) as dangerous, and fear it. Those who have been influenced by the people of Pulse (Outsiders), are quarantined by the "Holy Government" of Cocoon, and deported to Pulse. The prisoners shown in the E3 2006 trailer are being deported.
Final Fantasy versus XIII (action RPG)
As with every Final Fantasy, the ****of this world is unique, appearing to blend both modern and medieval aesthetics. The main character's country appears to be very advanced and modern, as one example, while neighboring countries appear to have remained in an era similar to the Middle Ages. The main power in the world are the Crystals. All the countries (aside from the protagonist's) have had them at one time, only to lose them in continual warfare. They had pooled their resources into weapons, granting them advanced rifles rather than swords and magic. Now, only the main character's country has a Crystal, triggering debate over its use as it is beneficial to the military. Recently, a peace treaty was discussed (Mentioned in the radio in the JF trailer). However, marauders with guns invade the city as the main character battles them, disrupting the peace.
Tetsuya Nomura has said "Versus XIII is supposed to resemble the modern-day world. I wanted to make this world resemble our world we live in today. This is integrated to the story as well but the reason I chose to use a Shakespeare quote at the beginning of the trailer is to make the tie with the real world we live today".
Final Fantasy agito XIII (mobile)
The game is set in a magic school named Akademia, and will gradually expand to the larger world outside of the school. It is described as an online RPG, but not "massively multiplayer". "Agito" in Latin roughly means "I engage in motion" (and is also the root from which the English "agitate" is derived).
There are twelve characters revealed, all twelve appear to be students. Weapons include longsword, katana, handguns, a shotgun, a mace, a bow and arrow, a spear, a scythe, an extending flail, bare fists, a flute and a deck of tarot cards. The Moogle, used in previous Final Fantasy games, is commonly mistaken as the 13th character. The character with the deck of cards has been revealed to have a greater importance than the other characters (shown in a pamphlet at the 2006 Tokyo Game Show).