It seems that at the Kotel, the general practice is to daven directly facing the wall. (Speaking from experience.) However, i thought we were supposed to face the kodesh hakodashim, which has a ...
"The Belzer Rebbe, Rebbe Ahazon, zatsal, when visiting the wall would search for a certain protruding stone. He would pray at that spot, explaining that his father, Reb Yissachar Dov, zatzal, had told ...