Another interesting conflict concerns Nick's feelings about Jordan Baker. He is very attracted to her. At the end of the novel, Nick goes so far as to say he was half in love with her. However, Nick regretfully rejects Jordan because he has come to condemn the values she accepts and the lifestyle she lives. Nick must go home to the Midwest to maintain his own identity and self-respect.
Also, the conflict between Tom and Daisy is very real, although most of it is subtle, quite below the surface. Tom has never been faithful to Daisy, even during the very earliest days of their marriage, and she has always known it. The tension between them flares occasionally, as it did in Chapter I when Nick is at their home for dinner. When Tom's mistress calls him at home, he takes the call, Daisy follows him into the house, and an argument ensues, although it is conducted in hushed tones and both of them continue the evening as if nothing had happened.
Tom continues to cheat, and Daisy renews her affair with Gatsby, perhaps an act of retribution on her part. Frequently, Daisy plays her role in her conflict with Tom through passive aggression. When she goes with Tom to one of Gatsby's parties, her behavior is not particularly discreet. Later, she flaunts her "friendship" with Gatsby by riding with him in his car, instead of with her husband, on the fateful trip to New York City. Her behavior does not go unnoticed by her husband who is clearly angered and upset by it. In the following hotel scene, however, Daisy's anger and resentment boil over. She attacks Tom for being such a hypocritical adulterer, telling him he is "revolting."
What about the conflict between Myrtle Wilson's lot in life and her desires to be part of the wealthy culture around her? She goes to a huge extreme to look the part, so to speak, even having an apartment stocked with expensive clothes to change into, just to appear wealthy to Tom, someone who will never respect her or see her as anything more than trash from the Valley of Ashes.
There's also a conflict of Nick Carraway trying to withold judgment, although he's unable to do so at times based on the amount of moral corruption he sees around him. Whether it's Daisy hitting and killing Myrtle with Gatsby's car, George killing Gatsby for apparently killing his wife, or Tom having a public affair with Myrtle, Nick cannot accept the things he sees as beneficial, and declares to Gatsby that he's worth "the whole damn lot of them put together".
You could talk about the culture clash between East and West Egg. You could also talk about how characters such as Daisy, Tom, and other wealty individuals become morally corrupt and how this conflicts with Gatsby's vision of the American dream.
I would also point you to the Enotes study guide for this novel: http://www.enotes.com/great-gatsby/themes