Jewish sources write that the Divine Presence rests upon the Western Wall. The Midrash quotes a 4th-century scholar: “Rav Acha said that the Divine Presence has never moved away from the Western Wall”. 18th-century scholar Jonathan Eybeschutz writes that “after the destruction of the Temple, God removed His Presence from His sanctuary and placed it upon the Western Wall where it remains in its holiness and honour”. Great Jewish sages, including Isaac Luria and the Radvaz, experienced a revelation of the Divine Presence at the wall.
(Wikipedia)
The Romans called the Second Temple in Jerusalem the most beautiful building in their empire. After they destroyed it in the year 70 of the common era only the Western retaining wall below the temple mount survived. Tradition relates that the presence of God hovers by the wall and has never left there. Jews have always mourned the loss of the temple and throughout the ages have sought to pray as close as possible to the site of the ancient temple. For the last 600 years Jews have prayed at the Western Wall.
Until recently the space provided for Jews to pray was limited to a small alleyway. But in 1967 Israeli armed forces liberated the Old City of Jerusalem from Jordanian rule which had forbidden freedom of worship to Israelis at the wall. Immediately after the war Israel razed buildings near the wall to create a large prayer plaza. If your schedule allows come to visit the wall before Friday night prayers when the Sabbath is greeted by Jews as a groom greets his bride.