I see that most people still wonder where the Hittites disapeared to. I have the answer to that.
The Hittites moved their capital to Babylon and eventually became Babylon the great, or the Babylonian Empire. Later to become the Persian Empire around the time of Cyrus.
I am pretty surprised that this isnt more widely known since this is all in the Bible.
You can look at the writing styles as well as the fashion styles from Babylon and see the strikng similarities with their predicecors from the Hattusha times.