Though we are told to do it, it often seems like a wasted effort to me. No peace will ever be had in Jerusalem without Jesus. But then praying for the peace of Jerusalem is asking for Christ to come for His bride, and after roughly seven years He will return with us, his bride, to end Satan's war on the Nations, establish His Kingdom, and bring the world to a forced peace. I say forced because like all the dispensations that precede His thousand year reign, it too will end in failure. Allow me to explain.
The First dispensation ended with Adam's sin against God, the result of which was man's expulsion from the Garden. The Second Dispensation ended with the Flood. The Third Dispensation ended with the Call of Abraham. The Fourth Dispensation ended with Israel going into Captivity in Egypt. The Fifth Dispensation was the Age of Law and ended with Christ Dying on the Cross. We are currently in the Sixth Dispensation, the Time of the Gentiles, and this, like all the previous dispensations, will end in failure.
The Seventh Dispensation-- the Earth's Sabbath Rest --also ends in failure. Man it seems has always pointed to this, that, and the other for the reason of his failure. But this time God will give Man no excuse. He will have Satan bound, and cast into the bottomless pit; locked away from the world for a thousand years. When Satan is released, it will take little time for Man to fall into evil and rebel yet again. The failure will not be God's, nor Jesus'. Rather the failure will be Man's, and this will be God's final demonstration to Man that he is indeed in need of a savior. What, did you think the Millennial Kingdom would be populated only by saved people?
Pray for Jerusalem. Pray for Israel. And pray for the Jews... Remember, they are still God's chosen people. By praying for them, and for Jerusalem, we do God's will.