As the previous answer pointed out, a central internal conflict is the conflict surrounding Quentin's feelings for Margo. He has idolized her, and he believes that he is in love with her; however, over the course of the novel, Quentin finally sees who Margo really is. The result is that he learns he can't make a life with Margo.

But I can’t say anything because she kisses me again, and it’s in the moment that she kisses me that I know without question that we’re headed in different directions.

There are some external conflicts in the book, too. A fairly straightforward external conflict is the conflict between Margo and her ex-boyfriend. Margo isn't just hurt over Jase's actions. She actually seeks out and takes revenge on him.

She pulled open the Lexus’s driver-side door, sat down in the seat, and proceeded to attach The Club to Jase’s steering wheel. Then she softly closed the door to the Lexus. “Dumb bastard never locks that car,” she mumbled as she climbed back into the minivan.

A bit later in the book, she explains her actions.  

"Because he’s been cheating on me for six weeks? Because he’s probably given me god-only-knows-what disease? Because he’s a disgusting idiot who will probably be rich and happy his whole life . . ."

I believe another external conflict surrounds Quentin. Internally, he does wrestle with his feelings for Margo; however, externally he struggles with actually finding Margo. A great deal of the book is about his quest to find Margo. The conflict is made tougher by the fact that the police and even Margo's parents don't seem too concerned about her. Their lack of concern means that they lack the willingness to help Quentin find her.

He took a few notes while I talked, but nothing very detailed. And something about telling him, and his scribbling in the notebook, and her parents being so lame — something about all of it made the possibility of her being lastingly missing well up in me for the first time.

He's left to solve the conflict without their help.

The central conflict of this novel is the journey that Quentin, the protagonist makes as he battles with his love and infatuation for Margo and comes to realise the difference between the Margo he loves and the real Margo who is actually shown to be a rather callous and unthinking individual, as shown by her night of pranks that she insists Quentin joins her on. In spite of Quentin's rather balanced life, apart from discovering a suicide victim with Margo, it is clear in the novel that Quentin's character is burdened by his youthful infatuation with Margo, and it is only when he embarks on his quest to "save" Margo that Quentin is forced to see that Margo is actually very different from how he imagined her to be:

The fundamental mistake I had always made—and that she had, in fairness, always led me to make—was this: Margo was not a miracle. She was not an adventure. She was not a fine and precious thing. She was a girl.

The conflict in this novel therefore is an internal one and centres on the perception of Quentin of his childhood love and the gap between appearances and reality. Thankfully, Quentin is able to see Margo for who she really is and therefore move on in life to a healthier position.

What are the conflict and resolution in Paper Towns?

In the novel Paper Towns, the conflict is twofold. Firstly, the external conflict—which begins, unconventionally, in the second act of the story—is Quentin's search for his friend Margo, who has gone missing. Quentin and his friends go on a quest to find her using clues that she had left behind. They succeed, but, rather than being ecstatic to see them again, Margo is surprised and insists on staying behind instead of returning home with them. This conflict can thus be considered ultimately unresolved.

The internal conflict revolves around Quentin and his love for an idealized version of Margo that exists only in his mind. Throughout the novel, which is narrated from Quentin's point of view, Margo is consistently described in romanticized terms. However, upon her disappearance, Quentin is forced to confront the fact that the real Margo may not live up to the perfect image of her that he has conjured for himself. This is further confirmed when Quentin gets angry at Margo for not wanting to return home with him and his friends, and Margo immediately retorts that he did not chase after her in order to help her, but rather in order to be the knight in shining armor who saves the troubled damsel and wins her heart in the end. Margo's running away forces Quentin to reconcile the Margo from the night during which they executed her revenge plan and the Margo who simply wanted to disappear into a town that existed only on paper. This conflict is resolved when Quentin comes to terms with the fact that he had idealized Margo, and the two of them part on civil terms at last.

What is the main conflict in Paper Towns by John Green?

One of the conflicts in Paper Towns is the conflict that Quentin feels between being a conventional and what he calls a "well adjusted" (page 6) rule follower on one hand and following what Margo does on the other hand. Even when they are nine and discover a dead body in their neighborhood, Margo wants to investigate, while Quentin wants to go home. When Margo forces Quentin to accompany him on a night of pranks to avenge what some of her friends have done to her, he is an unwilling accomplice. At the end of the book, even though Quentin has deviated from his routine to find Margo, he decides to return to his life rather than accompany Margo on her journey to New York City. In the end, Quentin decides to follow a more conventional life path rather than follow Margo on her uncharted adventures.

Margo, for her part, feels a conflict between what she is supposed to do and what she wants to do. Her conflict arises because she feels ill at ease in society and disconnected from the people around her, and her obsession with paper towns has to do with the superficiality she finds in her friends and family. She first calls Orlando a paper town (page 56), and then she becomes obsessed with finding these towns, which only exist on the map. When these towns appear in encyclopedias or on maps, they are intended to catch people who plagiarize or copy the maps without permission. For Margo, these towns represent the falseness in people she sees around her. Her reaction to this conflict is to continue to run away from home, eventually to a paper town in New York state and then to New York City. She has not necessarily resolved this conflict by the end of the novel, but she has made a real connection with Quentin that is different than the kinds of connections she had in Florida. 

Of course, as with any longer narrative such as a novel, there are more than one conflict, internal as well as external. But, the main conflict that propels most of the narrative is the condition of the relationship between Quentin and Margo.

After being childhood friends, Quentin Jacobsen, the protagonist, loses touch with Margo Spiegelman; however, Margo Spiegelman, re-appears one night at Quentin's house, inducing him to join her on a night of vandalism as acts of revenge. The two teens succeed in their daring mission which includes breaking into Sea World; however, after Quentin returns home and tiptoes to his room, his mind "booming with the things I would say to her at school" the next few days, he discovers that his childhood friend is missing.

Nonetheless, Margo has left some clues behind; so, Quentin elicits the aid of his friends Marcus, "Radar," Lacey, and Ben to help him find Margo. Having found Walt Whitman's volume of poems, Leaves of Grass, Quentin discovers clues to Margo's whereabouts, such as a map with holes that lead him to Algoe, New York. Along the way, there are some serious conflicts among the friends, even ones which could possibly lead "to the death of everyone," but all these conflicts are resolved when Quentin and his friends arrive and find Margo, who is writing in a black notebook. Surprised that they have traced her, Margo begins to explain. The final paragraph provides the resolution to the novel:

I feel her hands on my back. And it is dark as I kiss her, but I have my eyes open and so does Margo....even now there is an outward sign of the invisible light....our foreheads touch as we stare at each other. Yes I can see her almost perfectly in this cracked darkness.

Both Margo and Quentin have been wounded from their young experience of discovering Robert Joyner, who had killed himself in a park. But, now together "in this cracked darkness" of memory and trauma from their youth, they can heal each other.

The most significant conflict in the novel is the internal that both Quentin and Margo share. When they are both nine years old, they discover the body of a man who had died by his own hand lying in the park they had gone to play in. The rest of the story is about the internal conflict of how and how well they each adjust to this traumatic event.