There are five cities that these appear in.
Minas Ithril (Becomes Minas Morgul at the start of Act 2)
Gorgoroth
Nurnen
Seregost
Cirith Ungol
There are three in each city and you must complete it until the game tells you to exit the Haedir by pressing
NOTE: One in Seregost gave me trouble and I had to go back to mark the last Gondorian Artefact.