Let's examine some of the many conflicts of Stephanie Meyer's Twilight:
Person vs. Self (INTERNAL): When Bella meets Edward Cullen shortly after relocating to Forks, Washington, to live with her father, she is instantly drawn to the enigmatic young man. After a series of events in which Edward mysteriously is able to save Bella, Bella finds out the truth: Edward is a vampire. Although Edward warns Bella to stay away from him, the two fall in love. Their relationship, however, is never simple; both Bella and Edward experience a long internal struggle over whether to be with each other. Edward feels that he is placing Bella's life in danger and exposing her to his soulless existence by being in a relationship with her. Bella is deeply attracted to Edward as well, but is also pulled away by the presence of her less supernatural life (her father, Jacob, etc.). Despite the disapproval of many of those around them, Bella and Edward choose to take the risk of pursuing a relationship.
Person vs. Person (EXTERNAL): After James, a vampire who feeds on humans, spots Bella at the Cullen baseball game, he decides to hunt her down for fun. Edward and the Cullens do everything in their power to protect Bella, but James still manages to lure her to her old ballet studio by pretending that her mother is in distress. In an epic person versus person showdown, the Cullen family battles James to save Bella's life, and James is killed.
Person vs. Society (EXTERNAL): All vampires in the novel--and the Cullens in particular--face a continuous divide between their nature and the nature of society. This occurs on an external level in that the Cullens must live their lives in such a manner that shields their secret from the outside world; they move from city to city every few years to conceal the fact that they don't age, retreat from school when it is sunny enough to reveal their sparkling skin, and make other concerted efforts to appear human (blinking when they don't have to, etc.). Despite these actions, it is clear that they are outsiders in Forks and draw much gossip and speculation from the townspeople.
Of all of these conflicts, arguably the "main" one would be that of Person vs. Self... as the internal struggle that Bella and Edward both deal with through the book as to whether to be together (a conversation which eventually evolves into whether to be together with Bella as a vampire) continues throughout the rest of the Twilight saga.
I do not think that I could name one main conflict. I can name one main conflict type though. That would be the internal, person vs. self conflict. Both Edward and Bella face this conflict. Edward is deeply in love with Bella, but he knows that he should stay as far away from her as possible. He knows that his being a vampire will bring a lot of trouble for her, yet he wants to be with her with every fiber of his being. Likewise Bella is falling hard for Edward, and once she learns his true identity, she is conflicted with whether or not to pursue the relationship.
There is an external, man vs. man conflict in the novel. It would be the entire James plot line. James wants Bella dead, and Edward wants to protect Bella.