Annúminas (S. 'Tower of the West'; annún = west, minas = tower) was the city of the Kings of Arnor, on the shores of Nenuial. The city was founded by Elendil himself, on the shores of the northern lake Nenuial, near the sources of the Baranduin. It was the chief city of the Kings of Arnor for several centuries, and home to one of the three palantíri of the North-Kingdom.
The available evidence suggests that the city survived for nearly a thousand years. In the early days of Arnor, it must have been one of the glories of Middle-earth. Soon after its founding, though, the numbers of the Dúnedain of the North began to dwindle. The population of Annúminas seems to have fallen throughout its history, until eventually it was deserted, and the Kings removed to Fornost to the east.
It seems likely that the people of Annúminas were dependent on the River Baranduin for their contact with the outside world. While the Hills of Evendim surrounded the city to the west and south, the city's people could reach the other cities of the Dúnedain that lay along the river by boat.
After the city's desertion, it fell into decay, but two relics of its greatness survived: its palantír and the Sceptre of Annúminas. The palantír remained in Middle-earth for more than a millennium after the loss of its city, but was ultimately drowned with Arvedui in the cold northern seas.
The silver Sceptre of Annúminas was the symbol of Kingship in the North-kingdom. A very ancient artifact, it was originally the rod of office of the Númenórean Lords of Andúnië. Though it would have been removed to Fornost by the Kings, and eventually came to be kept by Elrond in Rivendell, it retained the name of its ancient home of Annúminas.
At the time of the coronation of Aragorn at the end of the Third Age, Annúminas had lain in ruins for more than two thousand years. There are hints in The History of Middle-earth and Appendix A though, that Aragorn refounded the city and may even have made it his capital. No definite statement on this matter appears in the canonical works, though, so this must be considered speculation.