pil·grim·age 
(pĭlgrə-mĭj)
(pĭlgrə-mĭj)n.
1. A journey to a sacred place or shrine.
2. A long journey or search, especially one of exalted purpose or moral significance.
intr.v. pil·grim·aged, pil·grim·ag·ing, pil·grim·ag·es
To go on a pilgrimage.