What would go into the Vatican City hosting the Olympics? The state is only a few square acres in size, yes, but with the diocese of Rome all around providing ventures, size should not matter too much.
The symbolism of the Greek Olympics being hosted by the Vatican would be great. It would be a modern, physical metaphor for the influence of Greek thought on the Christian tradition. The pagan Olympic flame would be relayed to Rome and be used to light not a cauldron, but a Paschal Candle.
So how would it play out? Of course, the opening and closing ceremonies would be held in St. Peter's Square. If the funeral of John Paul II showed us anything, it is that people are willing to come and stand in the square and the adjoining streets for hours to be a part.
What would go into an opening ceremony? Given the Olympics are a rather secular, materialist event, would the Vatican go so far as to celebrate Mass for the opening? What better way of uniting the world would there be than using some chanting and Latin to capture the hearts and minds of a world wide audience?
Then the Holy Father would bless all the athletes and send them out to sanctify their competitions by offering them up for the greater glory of God...