pilgrimage
n. C / Un. a journey to a holy or special place for religious reasons. It can also mean a trip you take to show respect for someone or something you admire.
n. a journey made to a sacred place as an act of religious devotion. In a secular context, it refers to a trip taken to a site of great personal or cultural importance.
Every year, thousands of people make a pilgrimage to the holy city.
The writer's fans often make a pilgrimage to his childhood home to see where he grew up.
The route has served as a path for pilgrimage for centuries, drawing travelers who seek spiritual renewal through the physical challenge of the long walk.
From Middle English pilgrimage. By surface analysis, pilgrim + -age.
Often used with the verb 'make' or 'go on'.