The Elven refuge ruled by Elrond in The Lord of the Rings is Rivendell.
Rivendell, also called Imladris, is a hidden valley east of the Misty Mountains. Elrond founded it in the Second Age after the destruction of Eregion, and it became a sanctuary for Elves and their allies. Its location helped protect it from the enemies dominating much of Middle-earth.
Bilbo Baggins visits Rivendell during the journey described in The Hobbit and later retires there after returning from his adventure. In The Lord of the Rings, Frodo recovers there after being wounded by the Witch-king, and the Council of Elrond decides what should be done with the One Ring.
Lothlórien is the woodland realm of Galadriel and Celeborn. Gondolin was a hidden city of the First Age, and Mirkwood is a vast forest kingdom. These places are distinct from Rivendell.