There are a couple of opinions about the matter but they mostly come under either two Cumorahs or one.
If you think there may be two of them, one in central America, and one in the west part of the State of New York, then you are in company with some BYU Scholars(1) and author Chris Heimerdinger.
Several Church Authorities (2) have described the Hill Cumorah as being near Palmyra, New York. The only one. Perhaps the best enunciation of this doctrine is from Joseph Fielding Smith, Doctrines of Salvation, 3 vols., edited by Bruce R. McConkie [Salt Lake City: Bookcraft, 1954-1956], 3:232 forward. Here are some highlights:
Within recent years there has arisen among certain students of the Book of Mormon a theory to the effect that within the period covered by the Book of Mormon, the Nephites and Lamanites were confined almost entirely within the borders of the territory comprising Central America and the southern portion of Mexico-the isthmus of Tehauntepec probably being the “narrow neck” of land spoken of in the Book of Mormon rather than the isthmus of Panama. . . .
It must be conceded that this description fits perfectly the land of Cumorah in New York, as it has been known since the visitation of Moroni to the Prophet Joseph Smith, for the hill is in the proximity of the Great Lakes and also in the land of many rivers and fountains. Moreover, the Prophet Joseph Smith himself is on record, definitely declaring the present hill called Cumorah to be the exact hill spoken of in the Book of Mormon.
Further, the fact that all of his associates from the beginning down have spoken of it as the identical hill where Mormon and Moroni hid the records, must carry some weight. It is difficult for a reasonable person to believe that such men as Oliver Cowdery. Brigham Young, Parley P. Pratt, Orson Pratt, David Whitmer, and many others, could speak frequently of the Spot where the Prophet Joseph Smith obtained the plates as the Hill Cumorah, and not be corrected by the Prophet, if that were not the fact. That they did speak of this hill in the days of the Prophet in this definite manner is an established record of history. . . .
Perhaps this matter could rest at this point, but the question of the territory now embraced within the United States having been in possession of Nephites and Lamanites before the death of Mormon, carries some weight in the determining of this matter. In the light of revelation it is absurd for anyone to maintain that the Nephites and Lamanites did not possess this northern land. While Zion’s camp was marching on the way to Jackson County, near the bank of the Illinois River they came to a mound containing the skeleton of a man. The history of this incident is as follows:
“The brethren procured a shovel and a hoe, and removing the earth to the depth of about one foot, discovered the skeleton of a man, almost entire, and between his ribs the stone point of a Lamanitish arrow, which evidently produced his death. Elder Burr Riggs retained the arrow. The contemplation of the scenery around us produced peculiar sensations in our bosoms; and subsequently the visions of the past being opened to my understanding by the Spirit of the Almighty, I discovered that the person whose skeleton was before us was a white Lamanite, a large, thickset man, and a man of God. His name was Zelph. He was a warrior and chieftain under the great prophet Onandagus, who was known from the Hill Cumorah, or eastern sea to the Rocky Mountains. The curse was taken from Zelph, or at least, in part-one of his thigh bones was broken by a stone flung from a sling, while in battle, years before his death. He was killed in battle by the arrow found among his ribs, during the last great struggle of the Lamanites and Nephites.”
And on it goes. It is well written with lots of documentation to show that the Hill Cumorah is only one hill, near Palmyra. The book uses some scientific and scriptural citations and information to show that this is so. Of course, to the doubter it will never be enough (just like it never is).
There are also several accounts of Joseph Smith and Oliver Cowdery returning the gold plates to the Hill Cumorah, this one is from the Journal of Discourses(3).
When Joseph got the plates, the angel instructed him to carry them back to the hill Cumorah, which he did. Oliver says that when Joseph and Oliver went there, the hill opened, and they walked into a cave, in which there was a large and spacious room. He says he did not think, at the time, whether they had the light of the sun or artificial light; but that it was just as light as day. They laid the plates on a table; it was a large table that stood in the room. Under this table there was a pile of plates as much as two feet high, and there were altogether in this room more plates than probably many wagon loads; they were piled up in the corners and along the walls. The first time they went there the sword of Laban hung upon the wall; but when they went again it had been taken down and laid upon the table across the gold plates; it was unsheathed, and on it was written these words: “This sword will never be sheathed again until the kingdoms of this world become the kingdom of our God and his Christ.”
Presumably, these are the records that Mormon hid up in the Hill Cumorah as referenced in the Book of Mormon although some people continue to say that there are only second hand accounts of the event, or that it may have been in vision and not in reality, or other such things.
On the one hand, scholars seek to find things based on the evidence that is present now while Prophets seek revealed truth from God. I’ll stick with what the Prophets have to say about where the Hill Cumorah is, and whether there is only one of it.
(1) John L. Sorensen, An Ancient American Setting for the Book of Mormon [Salt Lake City and Provo: Deseret Book Co., Foundation for Ancient Research and Mormon Studies, 1985], p. 44. Sidney B. Sperry, Book of Mormon Compendium, [Salt Lake City: Bookcraft, 1968] pp. 6-7.
(2) James E. Talmadge, Articles of Faith [Salt Lake City: Deseret Book Co., 1981], p. 231. B. H. Roberts, A Comprehensive History of The Church of Jesus Christ of Latter-day Saints, 6 vols. [Salt Lake City: Deseret News Press, 1930], 1: 75-76. George Reynolds, A Dictionary of the Book of Mormon [Salt Lake City: J. H. Parry].
(3) Journal of Discourses, 26 vols. [London: Latter-day Saints’ Book Depot, 1854-1886], 19:38-39.