When trying to determine William Shakespeare's concept of Prospero's Island in "The Tempest", we can look for clues in the text itself and some of the sources contemporary to the writing of the play (1610 or 1611).

Alonso's ship is bound for Naples in Italy when wrecked on an island.

Scholars have speculated that this Mediterranean island could be Pantalaria (Theodor Elze, 1889) or Corfu (William Bell, 1861).

William Shakespeare would have had access to documents relating to the exploration of the new world.

Two of these in particular;

A True Repertory of the Wreck and Redemption of Sir Thomas Gates, Knight, William Strachey, 1610

Discovery of the Bermudas otherwise Called the "Isle of Devils", Silvester Jourdain, 1610

are regarded as possible sources of influence for "The Tempest".

If we are to believe in the relationship between Shakespeare and these sources then Prospero's Isle may have been Bermuda.

If you follow some of the links on this page, you will see that there is some controversy about these theories.