The Turks were the ultimate enemy of Venice and Cyprus at the time of Othello. This allows Shakespeare some licence to vary his plot a little and move the story from the safety of Venice to the unknown realm of Cyprus. Shakespeare has been known for moving the action of his plays- such as in Antony and Cleopatra it moves from civilized Rome to unrestrained Egypt. In A Midsmmer Night's Dream, the magical world outside the seat of logic and reason is chosen to conduct much of the action.  

News has come to the Duke that a turkish fleet is headed for Cyprus and it is therefore necessary to send an army to defend it. Ironically it is Iago who is entrusted with Desdemona's safe passage there to meet her husband.

Consider Othello himself - although not a Venetian, he is a well-respected, decorated soldier. He moves from the civilized world of Venice where self-control is expected of him to a seemingly more passionate, unruly island. At first, even Othello's and Desdemona's behavior towards each other on the island is different and they are more relaxed and carefree. Othello is confident and arranges

a feast to honor the defeat of the Turkish fleet and to celebrate his marriage to Desdemona.

Othello then changes from a respected, self-controlled individual to one obsessed by jealousy.  

The drama that precedes the arrival on the island  “the wind-shaked surge, with high and monstrous mane,” a possible foreshadowing of what is to follow, adds to the drama and the potential of the island.

Desdemona is away from the safety of her family in Cyprus. She is passive and virtuous and her helplessness is reinforced by her presence on the island.

There are therefore several considerations regarding the setting. there's also the question as to whether Othello would have behaved in the same manner had they never left venetian society.