The Book of Mormon identifies three New Jerusalems:

1. Israel
2. America
3. Above

Israel

It was prophesied that the one in Israel would be rebuilt and thus becoming "new" which did happen in 1948.

America

The prophecy of one in America was hi-jacked by Joe Smith when he attempted to build one in Independence, Missouri. The prophecy read thus:

22 But if they [Gentiles] will repent and hearken unto my words, and harden not their hearts, I will establish my church among them,  and they shall come in unto the covenant and be numbered among this the remnant of Jacob [Indians], unto whom I have given this land for their inheritance;
23 And they [Gentiles] shall assist my people, the remnant of Jacob [Indians], and also as many of the house of Israel [Jews] as shall come, that they may build a city, which shall be called the New Jerusalem..
24 And then shall they [Gentiles] assist my people [Indians] that they may be gathered in, who are scattered upon all the face of the land, in unto the New Jerusalem.
25 And then shall the power of heaven come down among them; and I also will be in the midst.
26 And then shall the work of the Father commence at that day, even when this gospel shall be preached among the remnant of this people. Verily I say unto you, at that day shall the work of the Father commence among all the dispersed of my people, yea, even the tribes which have been lost, which the Father hath led away out of Jerusalem. (3 Nephi 21)

This New Jerusalem would be in place before the Book of Mormon came forth and is easy to identify: Whatever the government was over the land where the Book of Mormon came forth was the government of the New Jerusalem. That was the United States of America with her inspired Constitution.

Joe's attempt to build that prophesied New Jerusalem failed because:

1. The New Jerusalem was already built. (3 Nephi 21:22-26)
2. He threatend to have the land in Missouri "by purchase or by blood" which the Missourians resented and responded to by kicking the Mormons out. (D&C 63:29)

Mormons are still waiting to return to Independence to build Joe's idea of the prophesied New Jerusalem which they claim must be done before Jesus can return.

Above

Book of Mormon prophet Ether prophesied that the New Jerusalem from above would descend to ancient Book of Mormon land. 

2 After the waters had receded from off the face of this land it became a choice land above all other lands a chosen land of the Lord wherefore the Lord would have that all men should serve him which dwelleth upon the face thereof

3 and that it was the place of the New Jerusalem which should come down out of Heaven and the Holy Sanctuary of the Lord (Ether 13)

Mormons who believe that Book of Mormon events took place in Mexico/Guatemala/Malaysia/etc. need to expect this heavenly Jerusalem to descend there. Book of Mormon Christians on the other hand recognize that ancient Book of Mormon lands are where the record came forth; that Colonial America was the New Jerusalem for the New World and that the heavenly Jerusalem will come down to her.

Book of Revelation

1 And I saw a new heaven and a new earth: for the first heaven and the first earth were passed away; and there was no more sea.

2 And I John saw the holy city, new Jerusalem, coming down from God out of heaven, prepared as a bride adorned for her husband.

3 And I heard a great voice out of heaven saying, Behold, the tabernacle of God is with men, and he will dwell with them, and they shall be his people, and God himself shall be with them, and be their God.

4 And God shall wipe away all tears from their eyes; and there shall be no more death, neither sorrow, nor crying, neither shall there be any more pain: for the former things are passed away.

5 And he that sat upon the throne said, Behold, I make all things new. And he said unto me, Write: for these words are true and faithful.

6 And he said unto me, It is done. I am Alpha and Omega, the beginning and the end. I will give unto him that is athirst of the fountain of the water of life freely.

7 He that overcometh shall inherit all things; and I will be his God, and he shall be my son.

8 But the fearful, and unbelieving, and the abominable, and murderers, and whoremongers, and sorcerers, and idolaters, and all liars, shall have their part in the lake which burneth with fire and brimstone: which is the second death.

9 And there came unto me one of the seven angels which had the seven vials full of the seven last plagues, and talked with me, saying, Come hither, I will shew thee the bride, the Lamb's wife.

10 And he carried me away in the spirit to a great and high mountain, and shewed me that great city, the holy Jerusalem, descending out of heaven from God,

11 Having the glory of God: and her light was like unto a stone most precious, even like a jasper stone, clear as crystal;

12 And had a wall great and high, and had twelve gates, and at the gates twelve angels, and names written thereon, which are the names of the twelve tribes of the children of Israel:

13 On the east three gates; on the north three gates; on the south three gates; and on the west three gates.

14 And the wall of the city had twelve foundations, and in them the names of the twelve apostles of the Lamb.

15 And he that talked with me had a golden reed to measure the city, and the gates thereof, and the wall thereof.

16 And the city lieth foursquare, and the length is as large as the breadth: and he measured the city with the reed, twelve thousand furlongs. The length and the breadth and the height of it are equal.

17 And he measured the wall thereof, an hundred and forty and four cubits, according to the measure of a man, that is, of the angel.

18 And the building of the wall of it was of jasper: and the city was pure gold, like unto clear glass.

19 And the foundations of the wall of the city were garnished with all manner of precious stones. The first foundation was jasper; the second, sapphire; the third, a chalcedony; the fourth, an emerald;

20 The fifth, sardonyx; the sixth, sardius; the seventh, chrysolite; the eighth, beryl; the ninth, a topaz; the tenth, a chrysoprasus; the eleventh, a jacinth; the twelfth, an amethyst.

21 And the twelve gates were twelve pearls; every several gate was of one pearl: and the street of the city was pure gold, as it were transparent glass.

22 And I saw no temple therein: for the Lord God Almighty and the Lamb are the temple of it.

23 And the city had no need of the sun, neither of the moon, to shine in it: for the glory of God did lighten it, and the Lamb is the light thereof.

24 And the nations of them which are saved shall walk in the light of it: and the kings of the earth do bring their glory and honour into it.

25 And the gates of it shall not be shut at all by day: for there shall be no night there.

26 And they shall bring the glory and honour of the nations into it.

27 And there shall in no wise enter into it any thing that defileth, neither whatsoever worketh abomination, or maketh a lie: but they which are written in the Lamb's book of life. (Revelation 21)

 

The use of the word "city" has proven a stumbling block for Mormons to accept that the New World New Jerusalem is the United States of America and not what Joe attempted in Independence, Missouri. The heavenly Jerusalem however is quite large measuring 1500 miles square and is also called a "city."