In the movie, it is supposed to be taking place in what would now be Baghdad, yes as in Iraq. It used to be called Babylon, but thats another story.
The original story of Aladdin invloves an impoverished young ne'er-do-well named Aladdin, in a Chinese city, who is recruited by a sorcerer from the Maghreb (Maghreb refers to the North West region of Africa, Tunisia, Morocco, Libya, etc..), who passes himself off as the brother of Aladdin's late father; to retrieve a wonderful oil lamp from a booby-trapped magic cave. After the sorcerer attempts to double-cross him, Aladdin finds himself trapped in the cave. Fortunately, Aladdin retains a magic ring loaned to him by the sorcerer. When he rubs his hands in despair, he inadvertently rubs the ring, and a djinni appears, who takes him home to his mother. Aladdin is still carrying the lamp, and when his mother tries to clean it, a second, far more powerful djinni appears, who is bound to do the bidding of the person holding the lamp. With the aid of the djinni of the lamp, Aladdin becomes rich and powerful and marries princess Badroulbadour, the Emperor's daughter. The djinni builds Aladdin a wonderful palace - far more magnificent than that of the Emperor himself.
The sorcerer returns and is able to get his hands on the lamp by tricking Aladdin's wife, who is unaware of the lamp's importance. He orders the djinni of the lamp to take the palace to his home in the Maghreb. Fortunately, Aladdin retains the magic ring and is able to summon the lesser djinni. Although the djinni of the ring cannot directly undo any of the magic of the djinni of the lamp - he is able to transport Aladdin to Maghreb, and help him recover his wife and the lamp and defeat the sorcerer.