The geography lesson begins with the description of lands belonging to Lamoni’s father, the overking. Mormon specifically notes that the proclamation was sent to “all his people who were in all his land.”
That land was bordered by the sea on the west and on the east. Thus, Lamanite territory covers all the land between two seas. For those attempting to use this information to find Book of Mormon lands on a map, that suggests that the east-west dimensions from sea to sea cannot be that large. Very few ancient civilizations could cover extensive territories, and those known from the New World postdate the Book of Mormon.
The next geographic clue is the dividing line between Lamanite and Nephite lands. The Nephite lands are represented only by the land of Zarahemla at this point, though Mormon will add other descriptions that fit his later time, rather than this date. The dividing line is called a wilderness. Other texts tell us that the land of Nephi is at a higher elevation than the lands of Zarahemla.
Mormon mentions Manti which is “by the head of the river Sidon.” The phrase “running from the east towards the west” is anomalous in that it might describe the river Sidon, or it might describe the wilderness line itself. In any case, the typical understanding of the head of the Sidon is that it represents the source of the river. This reading is not only based on the common meaning of the “head” of the river, but also the fact that the Land of Nephi is higher and the land of Zarahemla lower. With the wilderness between, it is reasonable that at least some of that wilderness is also higher than Zarahemla. The Sidon is never mentioned in the land of Nephi, and is associated with the land and city of Zarahemla. The property of water has it flowing downhill, therefore, confirming the reading of it not only beginning in the strip of wilderness, but also that it flows roughly northward (reading the east to west phrase as referring to the wilderness rather than the river).
Mormon intentionally includes Manti because that is the typical route taken between the land of Nephi and the land of Zarahemla, and certainly was the reason that the city of Manti was built in that strategic location.