According to The Book of Mormon, the land of Amulon was located in the greater land of Nephi.
We first learn of the land of Amulon in the book when a group of the former priests of king Noah, led by a man named Amulon, escape with the 24 daughters of the Lamanites and began to settle and till the land. For a time they lived undiscovered until the armies of the Lamanites that had followed the people of Limhi got lost in the wilderness and stumbled upon the people of Amulon (Mosiah 23:30-31). Amulon, by authority of the Lamanite king, is made teacher over the people in the land Amulon and other areas (Mosiah 24:1).
The land Amulon is not mentioned again until some 35 to 60 years later in Alma 24:1. The Amalekites (probably Amlicites) and Amulonites, as well as some of the Lamanites living in the land of Amulon and other areas were not converted and were angry at those who were converted.