This is an interesting question. Venice is the city in which William Shakespeare's Othello begins, and it is a rather unique city at this time, particularly in light of the themes found in the play.
First of all, Venice was (and still is) a predominantly white city. While that fact might not matter much to most stories, it matters a lot in this one. As you know, Othello is a Moor, and that means he is a man of color. Because of that, everything he does is seen, considered, and judged much more intensely and certainly more critically than a white man's actions would be. Really, the only thing the Venetians respect and admire (or at least recognize and appreciate) is Othello's commanding military reputation. He has earned his position as commander and general because of his valor in war, and the Venetians need someone to protect them. In this role and in this city, he is a significant figure--except when he marries Desdemona. Because he is an outcast of sorts, his marriage to "one of them" is seen some kind of breach in protocol. Black men, even important ones, just do not marry white women, especially important ones.
Venice provides a natural environment for the figure of the Moor to be both revered and despised. According to Venetian law, the Venetian Republic's army general was required to be a foreigner. Since Shakespeare's Venetians reflect the mores of English society, it follows that Venetian society would admire Othello for his valor and leadership but still recoil at the notion of his marrying into its families
Another aspect of this setting is the fact that it was well known for its many prostitutes. While no Venetian ever considers Desdemona to be a prostitute, when Iago works his evil machinations, it is much easier for Othello to believe that his wife could be unfaithful because he knows prostitution is rampant in her home city and part of the culture she grew up with.
Cyprus, on the other hand, is known to be an island of love, one of the places held dear by Venus, the goddess of love. In this setting, the couple does seem to experience a change for the better in their relationship. Trust is developing and love is deepening. Things eventually go awry because Othello believes the lies, but in the beginning things are better. Of course Othello is sent to Cyprus to fight, so we should not be surprised that the fighting invades his own home. It is ironic that all of this fighting and death happens in a place known most for its connection to love.
While Desdemona's love for her husband is never in doubt to the audience, Othello's love for Desdemona wavers and eventually crumbles into murder. In the beginning of their time in Cyprus, however, he does love her, as evidenced by these these lines in Act III scene iii:
Excellent wretch! Perdition catch my soulBut I do love thee! And when I love thee notChaos is come again.
In general, both settings create a sense of impending doom (tragedy) because war is in the offing. Venice is a city that thinks little of the Moor (or any foreigner) aside from his military usefulness, and even the couple's move to Cyprus, an island of love, is not enough to outweigh the natural distrust of Othello's non-military life.