The Elven refuge where Elrond lives in J.R.R. Tolkien’s The Lord of the Rings is Rivendell.
Rivendell is a hidden valley in Middle-earth, situated east of the Misty Mountains. Tolkien also gives it the Elvish name Imladris, meaning a location associated with a deep cleft or ravine. Elrond founded the refuge in the Second Age and remained its lord for much of the Third Age.
The settlement is important in both The Hobbit and The Lord of the Rings. Bilbo stays there during his journey, and Frodo recovers there after being wounded by the Witch-king. The Council of Elrond later meets in Rivendell and decides that the One Ring must be taken to Mordor.
Rivendell is distinct from Lothlórien, another Elven realm ruled by Galadriel and Celeborn. Gondolin belongs to an earlier First Age story, and Mirkwood is a separate woodland kingdom.