In Beowulf, where is the battle with Grendel set?

Beowulf's first battle in the epic is set in the great Danish mead hall named Heorot. Heorot is described as the "foremost of halls under heaven" and has been under Grendel's control for the last twelve years. The malevolent Grendel has terrorized the great mead hall and slaughtered numerous brave soldiers, making Heorot uninhabitable and dangerous. The Danish king, Hrothgar, happily accepts Beowulf's arrival from Geatland and holds a feast in the mead hall to celebrate. That night, Beowulf and his men sleep in Heorot and Grendel arrives. After Grendel kills a valiant warrior, Beowulf attacks the monster and eventually defeats him in an epic battle. Unable to use weapons against the monster, Beowulf grapples with Grendel and ends up ripping the monster's claw, arm, and shoulder from his body. Grendel is mortally wounded during the battle and flees back to his mother's lair, which is at the bottom of a treacherous lake.

In Beowulf, the battle with Grendel is set at Heorot, the royal hall of Hrothgar, the Danish king. Prior to Beowulf's encounter with Grendel, the monster had engaged in regular pillaging of Heorot for a considerable length of time (about twelve years, in fact), and he wreaked considerable havoc on Hrothgar's subjects by violently devouring many of them.
The fact that Beowulf fights and defeats Grendel at Heorot is significant. Heorot can be seen to represent civilized order in the midst of wilderness, while Grendel can be seen as the chaotic force attempting to topple said civilization. As such, the fact that Beowulf defeats Grendel at Heorot signifies the return of established order in the face of chaos and disorder. Of course, Beowulf's efforts have only begun after his defeat of Grendel (he still has to face Grendel's mother and the dragon), but his battle at Heorot is his first major victory in the epic.