Where are the Mormon "relics"? There were several Sacred items that were buried with the Plates of Gold by the prophet Moroni:


  "Having removed the earth, I obtained a lever, which I got fixed under
  the edge of the stone, and with a little exertion raised it up. I
  looked in, and there indeed did I behold the plates, the Urim and
  Thummim, and the breastplate, as stated by the messenger. The box in
  which they lay was formed by laying stones together in some kind of
  cement. In the bottom of the box were laid two stones crossways of the
  box, and on these stones lay the plates and the other things with
  them." (JS–H 1:52)


Oliver Cowdery, David Whitmer, and Martin Harris, saw these items at Fayette, New York, in June 1829 (see Doctrine and Covenants Section 17)


  "Behold, I say unto you, that you must rely upon my word, which if you
  do with full purpose of heart, you shall have a view of the plates,
  and also of the breastplate, the sword of Laban, the Urim and Thummim,
  which were given to the brother of Jared upon the mount, when he
  talked with the Lord face to face, and the miraculous directors (Liahona) which
  were given to Lehi while in the wilderness, on the borders of the Red
  Sea." (D&amp;C 17:1)


According to the LDS church, where are these items now?
As far as I know, Joseph only received the Golden Plates, the Urim and Thumim, and the breastplate to which the Urim and Thumim was connected.

Joseph Smith - History 1:59


  59 At length the time arrived for obtaining the plates, the Urim and
  Thummim, and the breastplate.[...]


The view referred to in D&amp;C 17:1 is the vision that the Three Witnesses saw.

Our Heritage: A Brief History of The Church of Jesus Christ of Latter-Day Saints


  David Whitmer explained: “We went out into the woods, near by, and sat
  down on a log and talked awhile. We then kneeled down and prayed.
  Joseph prayed. We then got up and sat on the log and were talking,
  when all at once a light came down from above us and encircled us for
  quite a little distance around; and the angel stood before us.” This
  angel was Moroni. David said that he “was dressed in white, and spoke
  and called me by name and said ‘Blessed is he that keepeth His
  commandments.’ A table was set before us and on it the records were
  placed. The Records of the Nephites, from which the Book of Mormon was
  translated, the brass plates, the Ball of Directors, the sword of
  Laban and other plates.” While the men were viewing these things,
  they heard a voice that said: “These plates have been revealed by the
  power of God, and they have been translated by the power of God. The
  translation of them which you have seen is correct, and I command you
  to bear record of what you now see and hear.”


The Golden Plates (and the Urim and Thumim) were taken again by the angel, and the other things were never in Joseph's posession, as far as I am aware.