Where in Middle Earth is the Paths of the Dead?

The relevant information can be found in the Lord of the Rings wiki here:. The description places the mountains:

The White Mountains formed the northern boundary of Gondor and the southern boundary of Rohan except in their easternmost provinces, where Gondor's province of Anorien lay to the north of the mountains.

The entrance to the Paths of the Dead is described as Dwimorberg.

Harrowdale is described as being near the Snowbourn River, hence on your map, near where the mountains and the river intersect, Edoras.