I. Book of Mormon geography
The Church of Jesus Christ of Latter-day Saints does not take an official position on the geography of the lands in the Book of Mormon. No evidence has turned up in the Americas that confirms any of the Book of Mormon cities, nations, or battles. Several theories exist among Mormons as to where the Book of Mormon may have taken place. For a long time, a hemispheric model held sway, where all of North, Central and South America were the theater of the book. In recent times, theories about Central America have been most prominent, see this site for an example. Much of the artwork that you find based on the Book of Mormon shows palm trees, Aztec-looking warriors, and a generally Central American milieu. However, The text of the Book of Mormon necessitates that the United States is the location for its events.
The Book of Mormon has a lot to say about the lands where it claims its events occurred. In particular, it says many things about the future configuration of these lands, and what it says casts light on where we should think that these lands were located. What some of these Book of Mormon prophecies establish is that the text takes place somewhere within what is now the United States of America.
II.Established in this land
In the book of 3 Nephi, Jesus is speaking to a crowd of Nephites in the land called Bountiful. He prophesies of a sign that will occur, which will indicate that the gathering of Israel from dispersion is about to take place. The sign he prophesies is the coming forth of the Book of Mormon among “the Gentiles” (3 Nephi 21.2) which will teach them about the past existence of the Nephites and Lamanites “who are a remnant of the house of Jacob.” Next comes a long sentence that establishes where this will happen (with my comments in italics):
Verily, verily, I say unto you (the Nephites),
when these things (the Book of Mormon) shall be made known unto them (the Gentiles) of the Father,
and shall come forth of the Father,
from them (the Gentiles) unto you (the descendants of the Nephites and Lamanites);
For it is wisdom in the Father
that they (the Gentiles) should be established in this land,
and be set up as a free people by the power of the Father,
that these things might come forth from them (the Gentiles)
unto a remnant of your seed (the Nephites and Lamanites) […] —3 Nephi 21:3-4
“This land” is the one that will be inhabited by the Gentiles, the same Gentiles who will bring forth the Book of Mormon. These Gentiles will also be set up as “a free people.” As we know, Joseph Smith lived in the United States of America, and produced the Book of Mormon in the state of New York. Thus, the Jesus of 3 Nephi is saying that wherever Bountiful was, it was within the territory of the future United States. Mormons have often made this same identification. For example, Elder Mark E. Petersen commented on these verses in 1968:
You will recall that the Savior was talking to the Nephites about the Gentiles who would occupy this country in the latter days. He talked about the destiny of America, and explained why there would be a United States…this is God’s land. He raised it up specially as he has raised up no other nation (Ludlow 280-81).
III.The land of their inheritance
In 1 Nephi 13, there is an extended prophecy about the history of America and the coming forth of the Book of Mormon. This prophecy is a vision that Nephi sees somewhere between 600 and 592 B.C. It touches on someone who clearly seems to be Christopher Columbus (verse 12) and then touches on the Pilgrims and other colonists, describing the Revolutionary War. At one point, Nephi says, “I beheld many multitudes of the Gentiles upon the land of promise” (I Nephi 13.14). When he says “the land of promise” he is not referring to Biblical Israel, but rather to the land promised to Nephi’s father Lehi and his family, which is where they arrive when they flee Jerusalem and sail across the sea. So there is a one to one correlation between Nephi’s land of promise and the land that the multitudes of Gentiles in his vision inhabit.
Let me focus for a moment on I Nephi 13:30, again with my italics to elucidate what is being said:
Nevertheless, thou beholdest that the Gentiles who have gone forth out of captivity (English colonists),
and have been lifted up by the power of God
above all other nations,
upon the face of the land which is choice above all other lands (New England and the U.S.A.),
which is the land that the Lord God hath covenanted with thy father
that his seed should have for the land of their inheritance;
wherefore, thou seest that the Lord God
will not suffer that the Gentiles (Americans) will utterly destroy the mixture of thy seed,
which are among thy brethren (the Lamanites or American Indians).
To confirm even further that this was meant for the United States, God tells Nephi that he will bring forth unto these Gentiles, “much of my gospel,” in a passage that refers to the Book of Mormon. The Gentiles who receive the Book of Mormon are the Gentiles who inhabit Lehi’s land of promise, meaning they are citizens of the United States. Again, the LDS Church’s own teaching manuals confirm this, as the Book of Mormon Student Manual discusses the United States in its commentary on this passage, citing the words of Joseph Fielding Smith:
This great American nation the Almighty raised up by the power of his omnipotent hand, that it might be possible in the latter days for the kingdom of God to be established in the earth (Book of Mormon Student Manual 13).
Although some modern Mormon apologists want to look elsewhere for the geography of Nephite lands, they should be confined to the United States, because that is what the text itself says.
Church Educational System. Book of Mormon Student Manual. N.p.: The Church of Jesus Christ of Latter-day Saints, 1989. Print.
Ludlow, Daniel H. A Companion to Your Study of the Book of Mormon. United States: Shadow Mountain, 1 Aug. 1976. Print.