The land of Noah first appears in The Book of Mormon record, ca. 81 B.C. After obliterating Ammonihah, Lamanite armies made depredations in the land of Noah. Ten years later, ca. 72 B.C., the city and land of Noah again appear in the text, also in the aftermath of a military action aimed at Ammonihah. The numbers 1 - 5 highlighted in aqua below are characteristics of Noah that will help us site it on the modern map.
The land of Noah was reasonably close to 1 the land of Ammonihah. Noah bordered wilderness 2, and the borders of Noah were populated. 3 Noah had a relationship with Manti - they are the only polities in the Nephite domain described as "weak" Alma 43:24, Alma 49:14-15. This implies that Noah and Manti were reasonably close to each other. 4 Noah was between the land of Ammonihah and the local land of Nephi because the Lamanites marauded around Noah as they were returning back from Ammonihah to the local land of Nephi. 5 ...