I think that most of the conflicts surrounding John Proctor are internal. One internal conflict of John's is his guilt. John is a respected and well liked member of the Salem community. People look up to him and believe that he is a good man. While John probably agrees with most of that about himself, he is conflicted with guilt about his sexual relationship with Abigail Williams. John tries to be a Godly and religious man, but he he knows that he has committed a great sin against God and his wife.
Another internal conflict of John's occurs at the very end of the play. Should he confess to a lie and live? Or should he die as honorable of a man as he can? It's an incredible scene, and in the end John chooses death in order to preserve his goodness.
Elizabeth, supporting herself against collapse, grips the bars. of the window, and with a cry: He have his goodness now. God forbid I take it from him!
External conflicts are a bit more difficult with John and this play. He's never really in any kind of battle against a person. At least not in the kind where punches are thrown or the kind in which a reader would be able to declare a winner. John has an external conflict with Abigail. She still clearly desires to continue their affair, but John is committed to never cheating again.
Proctor: Abby, I may think of you softly from time to time. But I will cut off my hand before I'll ever reach for you again. Wipe it out of mind. We never touched, Abby.
John also has an external conflict with Judge Danforth. In the final act of the play, Danforth is pushing John hard to name the people that he saw communing with the devil. Proctor does not want to confess to any more lies, so he doesn't give Danforth any names. The scene continues to intensify as Danforth all but forces John to physically sign a document of confession. Danforth wants to hang the document for all the world to see, and John doesn't want that. He doesn't want his good name tainted for all of Salem to see, so John eventually tears the paper up, which prevents Danforth from "winning."
His breast heaving, his eyes staring, Proctor tears the paper and crumples it, and he is weeping in fury, but erect.