The vicarage is a house. It doesn't live anywhere because it is not alive. It is what you call the house where a vicar lives. Like the house where a parson lives is a parsonage.
A vicarage or rectory
Vicars usually live in a Vicarage.
Vicars usually live in a Vicarage.
In a rectory. But a vicar lives in a vicarage.
The vicarage is typically the residence of a vicar, who is a cleric in the Anglican Church responsible for a parish. Often, the vicar may live there with their family, and it may also serve as a space for church meetings and community activities. The vicarage is closely associated with the local church and its congregation.
Vicarage Road
Cockerham Vicarage was created in 1843.
Polesworth Vicarage was created in 1870.
Halton Vicarage was created in 1739.
The Murder at the Vicarage was created in 1930-10.
Originally, the priest who was overseeing a church was called a Vicar. The residence for him was called a vicarage. Then, they called the priest overseeing a church a Rector. The residence for him was called a Rectory. Priests still live in a rectory nearby his church.
A vicar lives in a vicarage and a minister (Church of Scotland) lives in a manse.