The island kingdom where Aragorn’s ancestors lived in J.R.R. Tolkien’s mythology is Númenor.
Númenor is a great island realm established in the Second Age for the Men who aided the Elves during the wars against Morgoth. Its inhabitants, the Númenóreans, received unusually long lives and developed a powerful maritime civilization. Elros, the first king, was the brother of Elrond and chose the fate of Men.
Númenor was eventually destroyed after its king, Ar-Pharazôn, challenged the Valar and sailed against the Undying Lands. The catastrophe reshaped the world and left survivors who established realms in Middle-earth, including Arnor and Gondor. Aragorn descends from that royal tradition through the northern line.
Valinor is the realm of the Valar, Beleriand belongs chiefly to the First Age, and Eriador is a region of Middle-earth. These names are related to Tolkien’s geography but are not Númenor.