The forest where Legolas’s father rules in J.R.R. Tolkien’s Middle-earth is Mirkwood.
Legolas is the son of Thranduil, the Elvenking of the Woodland Realm in northern Mirkwood. The forest was formerly known as Greenwood the Great, but it became corrupted by the presence of the Necromancer, later revealed to be Sauron.
Mirkwood is a major setting in The Hobbit. Bilbo and the Dwarves travel through it, encounter giant spiders, and are captured by Thranduil’s Elves before escaping toward Lake-town. The forest also appears in the wider history of the Third Age.
Lothlórien is ruled by Galadriel and Celeborn, while Fangorn is the ancient forest associated with Treebeard. Beleriand belongs mainly to Tolkien’s First Age narratives.