E3 Demo Part 1 (Overworld):
Legend of Zelda: A Link Between Worlds - Overworld Tour Gameplay Footage (E3 2013) - YouTube
E3 Demo Part 2 (Dungeon):
Legend of Zelda: A Link Between Worlds - Dungeon Gameplay Footage (E3 2013) - YouTube
Don't take these for what the final game's content will be. With how close the heart pieces are to each other in the overworld and how the entrance to the Eastern Palace dungeon actually brings you to the "Tower of Hera"-based dungeon, this is probably not what the final game will be.
This game is not ALttP's "Master Quest" as they've said clearly that it is a sequel and the new story comes after ALttP. The way they've described the game being set in the same world as ALttP reminded me of Golden Sun and Golden Sun 2. I imagine we'll be seeing many familiar areas (like those shown) as well as many new ones that they just aren't willing to show right now. Hence why the demo's overworld is a very familiar area that leads to a dungeon that should come at a later point in the game, but was used earlier because it showcases the new wall-drawing and sense-of-height mechanics. The world map on the bottom screen is also blocked out with clouds so we won't be able to see any other areas.
Random speculation time: Maybe Link finds his way back to the ALttP Hyrule in the beginning of the game (after his adventures in Link's Awakening) only to find the peaceful land he left has turned to chaos without him there. Perhaps some evil character managed to grab hold of the Triforce from the King and ended up trying to merge the two worlds or something, drastically altering the landscapes of both.
OR (my favorite idea) maybe it's set in the same world, but a few generations down the line with a descendant of the ALttP Link and tells the story of the end of the
Golden Era where the current King decides to hide the Triforce of Courage before passing away. Your enemy can be his successor, the
Prince of Hyrule and his adviser the Magician in their search for the Triforce of Courage. The Magician is the one who puts Zelda in her eternal sleep after she wouldn't give up the Triforce of Wisdom, but all the story says is that "he dies immediately after" doing so. The Prince orders that every girl in the Royal Family shall hence forth be named Zelda so this tragedy is never forgotten. The Triforce of Power is the only piece whose location is known at this point. Courage was hidden by the late King (and maybe this new Link?) and Wisdom's location was known only to sleeping!Zelda at this point.
Many years later Ganon is revived and attacks Hyrule, stealing the Triforce of Power. There is a new Zelda in the Royal Family who has a nursemaid named Impa and has also found the Triforce of Wisdom. She splits it into 8 pieces so Ganon couldn't get his hands on it. Another boy named Link saves Impa and then the events of
The Legend of Zelda happen, with Link restoring the Triforce of Wisdom and defeating Ganon. The kingdom now has both the Triforce of Power and the Triforce of Courage.
Six years later the events of
The Adventure of Link happen. Ganon's leftover forces were still terrorizing Hyrule and trying to revive their master. Link embarks on a quest with six crystals, given to him by Impa, that need to be placed in statues in dungeons around Hyrule in order for the spell over the location of the Triforce of Courage to be lifted. (Perhaps A Link Between Worlds has Link helping the past King of Hyrule set up this spell using some of the crystals passed down through the Royal Family from ALttP. Link helps him hide the Triforce of Courage and then deals with the fallout this causes after the Prince ascends to the throne with his Magician adviser that eventually leads to Zelda II.) So there are two Zeldas in this timeline now. One is a descendant of the Royal Family and is the one Link saves in Zelda I and the other is sleeping!Zelda from the past with the Prince, who Link saves in Zelda II after finally restoring the Triforce.
TL;DR: I think this new game has a cool possibility of bridging the gap between the ALttP+OoA/OoS+LA storylines and Zelda I+Zelda II. A new Link helps a future King hide the Triforce of Courage by traveling to the different dungeons using the crystals to set up a spell and then defeats the angry Prince and his evil Magician, but not before Princess Zelda is put under the sleeping spell that only gets broken many years later after the decline of Hyrule.