Mark 16:5 Entering the tomb, they saw a young man sitting at the right, wearing a white robe; and they were amazed. 6 And he *said to them, “Do not be amazed; you are looking for Jesus the Nazarene, who has been crucified. He has risen; He is not here; behold, here is the place where they laid Him. 7 But go, tell His disciples and Peter, ‘He is going ahead of you to Galilee; there you will see Him, just as He told you.’” 8 They went out and fled from the tomb, for trembling and astonishment had gripped them; and they said nothing to anyone, for they were afraid.The subsequent verses are generally recognised to be a later addition.
So what we have is a guy in white, perhaps an angel, telling the women that Jesus would see the disciples in Galilee. Not only does the original not mention Jesus being in Jerusalem, it specifically indicates Jesus was not there. Why would the man send the disciples to Galilee if Jesus was to meet them in Jerusalem?
And this fits with what Jesus had said earlier:
Mark 14:27 And Jesus *said to them, “You will all [k]fall away, because it is written, ‘I will strike down the shepherd, and the sheep shall be scattered.’ 28 But after I have been raised, I will go ahead of you to Galilee.”This is in Matthew too:
Matthew 26:31 Then Jesus *said to them, “You will all [i]fall away because of Me this night, for it is written, ‘I will strike down the shepherd, and the sheep of the flock shall be scattered.’ 32 But after I have been raised, I will go ahead of you to Galilee.”The shepherd in this metaphor is clearly Jesus, and the sheep are his disciples. Jesus is saying that when he dies, his disciples will be scattered, but that he will see them again in Galilee. According to the gospel accounts, though, they did not scatter. They were supposedly still in Jerusalem when the empty tomb was found, and they remained there, as a group, where they met Jesus. The scattering is a remnant from an early narrative.
What probably happened is the prophecy got added to the narrative to fit what actually happened, and then the account of what happened got embellished so the prophecy subsequently became wrong!
Matthew stays closer to the original narrative, with a brief glimpse of Jesus, before they meet again in Galilee, and no suggestion of any other sightings than that.
Luke and Acts skip the whole Galilee trip altogether, with Jesus in and around Jerusalem. But then, Luke was writing for a gentile audience, and a cosmopolitan setting like Jerusalem would be far preferable to a cultural backwater like Galilee.
John does likewise, except for chapter 21, which looks very much like a later addition, apparently harking back to the earlier tradition.
All this points the the sightings in Jerusalem to being embellishments, made up some time after the Gospel of Mark, when the people who were around at the time could be assumed to be dead, and so unable to say otherwise.
A quick note about Matthew 28:17:
17 When they saw Him, they worshiped Him; but some were doubtful.Some were doubtful? I have seen the claim that what they doubted was whether they should worship Jesus or not, rather than whether it was Jesus or not. I think the text is sufficiently ambiguous that we cannot say one way or the other, so would not use this as evidence against Christianity (of course, if this was God's inspired word, we would expect it to not be ambiguous, but that is a lot different argument).
A quick note about Peter:
It is not canonical, but some scholars think the Gospel of Peter was earlier than Mark.
 And having gone off, they found the sepulcher opened. And having come forward, they bent down there and saw there a certain young man seated in the middle of the sepulcher, comely and clothed with a splendid robe, who said to them:  'Why have you come? Whom do you seek? Not that one who was crucified? He is risen and gone away. But if you do not believe, bend down and see the place where he lay, because he is not here. For he is risen and gone away to there whence he was sent.'  Then the women fled frightened.http://www.earlychristianwritings.com/text/gospelpeter-brown.html
 Now it was the final day of the Unleavened Bread; and many went out returning to their home since the feast was over.  But we twelve disciples of the Lord were weeping and sorrowful; and each one, sorrowful because of what had come to pass, departed to his home.  But I, Simon Peter, and my brother Andrew, having taken our nets, went off to the sea. And there was with us Levi of Alphaeus whom the Lord ...
This agrees with Mark, that subsequent to crucifixion, Jesus was first seen in Galilee, and not in Jerusalem (the ending of the gospel is missing; we only get a hint of this first sighting). It is interesting that the sighting by Peter on the fishing boat fits with the tacked on chapter in John.