In short, Venice represents civilization and order in Othello, and Cyprus symbolizes barbaric actions and chaos. In Venice, the Duke uses logic to rectify the situation with Othello and Desdemona's elopement; in Cyprus, Iago uses emotional manipulation to destroy relationships. In Venice, Othello and others like Brabantio handle their disagreements civilly in the Duke's Palace. In Cyprus, physical fights break out between Montano and Cassio and Roderigo and Cassio.
Shakespeare juxtaposes the two settings to demonstrate what happens to a person when he allows his emotions to rule him rather than his logic. For example, in Act I when Othello is in Venice, he will not allow Brabantio to goad him into a fight, but when he gets to Cyprus, an isolated military outpost, he soon falls prey to Iago's psychological manipulation and gives in to a hot temper and jealousy.
At the play's end, even though the physical setting of Act 5 is still Cyprus, notice how the visitors from Venice (Lodovico and Gratiano) are the ones to restore order after all the chaos and death. It is as if the play ideologically concludes in Venice.
The settings in Othello and what each represents is ironic. Firstly, Venice represents that which is supposedly good - law and order, a structured and civilized way of life. Venice is a place in which one can depend on the powers-that-be to defend one's rights and provide one with a voice to speak out against prejudice or unfair discrimination. It is in Venice that Othello and Desdemona's love is born and where it flourishes. It is ironic, therefore, that it is in Venice that Iago formulates his pernicious plot to destroy Othello. Furthermore, it is also in Venice that Brabantio, Iago and Roderigo display their racist prejudice.
Since Venice is a symbol for rational thought and reason (i.e. order), it is ironic then, that Brabantio loses all reason and allows prejudice to taint his judgment. However, it is also in Venice that Othello is afforded justice through the Duke's intervention, when he is allowed to defend himself and is vouched for by Desdemona. Further irony lies in the fact that although Venice is deemed a symbol of the civilized world, it is here that corruption is rife - Roderigo, for example, thinks nothing of plying, at Iago's insistence, Desdemona with gifts to win her affection.
Furthermore, Venice is also known for its courtesans, a place in which loose women freely plied their trade, to such an extent that even Emillia intimates that she would sell her affections if the money were right.
Cyprus, as a contrast to Venice, is where danger lies. Cyprus represents disorder and chaos. As a military outpost, it is constantly at war - defending itself against many attacks. This means that its citizens are constantly ill-at-ease, either because of actual, imagined or impending threats. Unlike Venice then, which represents stability, security and peace, Cyprus is in constant turmoil. It is therefore ironic that Cyprus is believed to be the birthplace of Aphrodite, the goddess of love.
It is in Cyprus that Iago brings his evil plot to fruition and it is here, amidst all the uncertainty, that Othello and Desdemona's fates are sealed. Instead of their love flourishing, they are doomed because of Iago's treachery and manipulation. It is also in this setting where the leading characters turn against each other and where they meet their doom. In this context then, Cyprus provides the ideal backdrop for Iago's evil to flourish.
Are there any direct quotes from the book that prove this symbolism of the settings?