Shaikhul Islaam Ibn Taymiyyah (rahimahullaah) said:

Abu Bakr, Umar, Uthmaan, Ali and all those who were foremost to embrace Islaam of the Muhaajiroon and the Ansaar used to depart from Madeenah to Makkah to perform Hajj and Umrah, and as travellers; but it is not stated that a single one of them strove to pray at (any particular) spots in which the Prophet (sallal-laahu-alayhi-wasallam) prayed.  And it is well-known that if this (practice) was something they considered recommended, they would have been more worthy to precede in it; because they were more knowledgeable about his Sunnah and followed it more than others.

[Source: Iqtidaa Siraat Al-Mustaqeem 2/748]