Is there any relevance today for the Christian in Jerusalem because there are those that place great emphasis on that place.?

No more significance than anywhere else in the world. Jews can be Christians too if they place their faith and trust in Jesus Christ's death, burial, and resurrection as payment for their sins just like anyone else.

Jerusalem and the surrounding areas will once again be a large part of Israel's history. After the Tribulation, Jesus will come back to earth to set up the Kingdom. The promise God made to them through Abraham. It will last for a 1,000 years or a millennium thus sometimes called the Millennial Kingdom. It also plays a big part for the true believers that were raptured before the Tribulation. The Church/Saints/Christians (all synonymous) will rule and reign with Jesus Christ during this 1,000 year period.

I don't know that a certain place on earth should have ever been the focus and object of desire of the big three. All are supposed to worship god and Christians add the son but still they all what that peace of land. It's been quite some time since the Christians made a move for it but I would imagine they will when they see an opportunity.

All focus will be on Israel, it plays a huge part in prophecy fulfillment, even currently. The Jews are being regathered and they're preparing to rebuild the Temple. Christians will definitely have to be careful. Things in Israel will become increasingly dangerous.

Since the descriptions of a fabricated story cannot be physically found, it was carefully mentioned not to be worried about the place.

I'd like to go. Then again, I'm not really big on suicide bombers or terrorist attacking at any given moment, so I suspect what they have over me is more bravery.