Beyond the Veil by *Avender on deviantART Sirius Black and James Potter reunited again! So Harry saw Kings Cross because that was where he could escape from the normal world to Hogwarts. Sirius escaped from Hogwarts to his friends.
I really love this moment in the books. I don't think Dumbledore was trying to make Harry feel better, I think he genuinely thought Harry had become a good, brave man and Dumbledore truly felt better he had such a companion,