The chief city was at Fornost on the North Downs, but the old capital of Annúminas perhaps remained important;1Bree lay on the southern borders of the realm
The westernmost region of the lost realm of Arnor; when that land was divided between the sons of Eärendur, Arthedain became a kingdom in its own right, and was ruled by Eärendur's eldest son Amlaith and his decendants.
Notes
1
The Kings of Arthedain left Annúminas for Fornost as their royal seat, but the former royal city remained within the borders of Arthedain, and we're not told that it was entirely abandoned. We have no details of the history of Annúminas during this period: it might very well have continued to be a prosperous city during the time of Arthedain, or it might have fallen entirely into ruin.