But Peter rose and ran to the tomb; stooping and looking in, he saw the linen cloths by themselves; and he went home marveling at what had happened.
Luke 24:12 ESV

The Greek doesn't actually say that Peter went to his home, but that he "went back to his own". "Home" was added by the translators. His house was in Capernaum, but in the next few verses he is back with the other disciples, so he couldn't have gone home. It should say, "He returned to his place, marveling at..." or as the KJV has it "he departed, wondering in himself..."