The Hill of the Eye, one of the three peaks at the end of the long lake called Nen Hithoel on the Anduin River.

The other two were Amon Lhaw (or the Hill of the Ear) on the eastern bank, and Tol Brandir, an unclimbable island pinnacle that stood in the centre of the lake.

Amon Hen and Amon Lhaw had on their summits two magical thrones were called the Seat of Seeing on Amon Hen and the Seat of Hearing on Amon Lhaw.

During the War of the Ring, the Fellowship of the Ring made their way to the bottom of Amon Hen. There, Frodo Baggins sat upon the Seat of Seeing and discovered its magical properties by suddenly being able to see for hundreds of miles in all directions.
Encyclopedia entry originally written by High_King_Of_Gondor