Jesus' tomb
We know the burial places of most early Christians, except one: Jesus himself. If you believe that the body of Jesus disappeared when he ascended to heaven, as the Church does, you don't have to explain where his bodily remains are. Everybody else should at least wonder why we haven't found the tomb of the very man who is at the center of the Christian faith (the four official gospels list four different burial places). Jesus' date of birth and death are also disputed. Herod died in 4 BC, so (if the gospels tell the truth) Jesus can't be born after that date. The Acts of Thomas record that Jesus was in Taxila at a marriage ceremony in the year 49. Irenaeus himself (not a heretic) writes that Jesus reached an old age.
Was Jesus still alive when James the Just, Paul, Peter and Taddeus were spreading Christianity around the world?
The historian Jesophus mentions a "Jesus" who was alive during the years of the Jewish war (66-70 AD), who was an oracle and who was tried in front of Pilate (except that Pilate released him, not crucified him).
If the body of Jesus was buried somewhere, at least two people must have known and visited that place: his mother and his closest friend.
Mary (the mother of Jesus, James the Just and Taddeus) is known to have traveled to Turkey and may have died near Ephesus (according to local legend). James was almost certainly with her. They were, de facto, exiles.
Mary Magdalene was closer to Jesus than anyone else. "Miriam" was the "apostle of the apostles", and the first witness of the resurrection. The gospels give different accounts of her whereabouts and movements before and after the death of Jesus. There is a legend that she traveled to France, to La Sainte-Baume (near Marseilles), and lived in solitude in a cave for the rest of her life. There is a legend that she followed the Virgin Mary to Turkey and died there.