Macduff doesn't go to Scone, the place where Macbeth will be crowned King of Scotland, because even at this fairly early stage in the play, Macduff already has some sneaking suspicions regarding Macbeth. These started to emerge in Act 2, Scene 3 ,immediately following the discovery of Duncan's body. After Macbeth returns from Duncan's chamber, he reports that he killed the two guards who are suspected of the murder. As soon as Macbeth says this, Macduff asks "Wherefore did you so?" At this point Macbeth begins to try to make up a reason for killing the guards, but his explanation goes on and on until Lady Macbeth feigns fainting and all eyes turn to her.
In Act 2, Scene 4 Macduff's disgust with the situation becomes even more apparent. Upon being asked how the day is going, he responds "Why, see you not?" Also, when Ross asks him the details of the murder, Macduff states the "official" story in a very matter of fact way. He says that those who killed Duncan were "Those that Macbeth had slain" and goes on to say that the guards were bribed. Further, he states that because Malcolm and Donalbain have fled, "suspicion of the deed" has been placed on them. If Macduff truly believed the official story, he would no doubt go to Scone to see Macbeth invested. Instead, he chooses to go back to his own castle, thus establishing the first moment that Macbeth will later reflect on to convince himself of Macduff's disloyalty, which in turn puts into motion the events that will lead to the climax of the play.