Does Galadriel wear any specific jewelry that is mentioned in the books?
Please include answers specifically from the books not just from the movies.
While it's unclear as to what she came to possess, in ages passed there existed a stone of great beauty called the Elfstone. It was supposedly crafted by Enerdhil (but may have been Celebrimbor, either the first, and only, or both editions).
There was in Gondolin a jewel-smith named Enerdhil, the greatest of that craft among the Noldor after the death of Fëanor... And it came into his heart to make a jewel within which the clear light of the sun should be imprisoned, but the jewel should be green as leaves. And he made this thing, and even the Noldor marvelled at it. For it is said that those who looked through this stone saw things that were withered or burned healed again or as they were in the grace of their youth...
Unfinished Tales: The History of Galadriel and Celeborn, The Elessar
This stone passed from Enerdhil to Idril to Eärendil who carried it across the Sea to the Undying Lands.
This is where the tale of the Elessar splits, there are two possibilities, "though which is true only those Wise could say who now are gone." (ibid.)
The first is that the Elessar returned as a gift from the Valar Yavanna with Olórin and was gifted to Galadriel.
"It is not so," said Olórin. "Their eyes are not dimmed nor their hearts hardened. In token of which look upon this!" And he held before her the Elessar, and she looked on it and wondered. And Olórin said: "[The Elessar] I bring to you from Yavanna. Use it as you may, and for a while you shall make the land of your dwelling the fairest place in Middle-earth.
While not explicitly stated, if it is indeed the same Elessar, it is more than likely Galadriel carried the stone on her breast, as did Eärendil.
The second, is that Celebrimbor (before his teaching/corruption by Annatar (Sauron)) produced, out of his love for Galadriel, a "replica" of the Elessar originally produced by his friend Enerdhil. While not the same as the original, the replica provided Galadriel the ability to keep at bay the fading of the beauty of the lands about her.
"That is its fate, I deem," said Celebrimbor. "But you know that I love you, and for that love I will do what I can, if haply by my art your grief can be lessened." But he did not say to Galadriel that be himself was of Gondolin long ago, and a friend of Enerdhil, though his friend in most things outrivalled him. ... And it is said that more subtle and clear was the green gem that he made than that of Enerdhil, but yet its light had less power... Radiant nonetheless was the Elessar of Celebrimbor; and he set it within a great brooch of silver in the likeness of an eagle rising upon outspread wings." Wielding the Elessar all things grew fair about Galadriel, until the coming of the Shadow to the Forest.
Given Celebrimbor set the stone within a great brooch, and Galadriel wielded the stone, it is likely she openly wore the brooch.
NB: And the end of the essay titled The Elessar, a note is made that Celebrimbor was the creator of both the original Elessar and the latter Elessar for Galadriel. This is likely the final version of the tale as Enerdhil is not seen elsewhere in the Legendarium
Although Galadriel possessed the Elessar, she passed it on to her daughter after Celeborn had sent her Nenya. So the Elessar came to Aragorn, through Celebrían and Arwen (ibid.). Nenya however wasn't a piece of jewellery that Galadriel openly wore, technically. While it was certainly a gemstone in a ring, it provided a means to an end, a secret means, and was more akin to a tool/weapon than jewellery. The Rings were invisible to all those but the bearers and the bearer of their master.
Yes,' she said, divining his thought, 'it is not permitted to speak of it, and Elrond could not do so. But it cannot be hidden from the Ring-bearer, and one who has seen the Eye.
Fellowship of the Ring - Book 2, Chapter VII: The Mirror of Galadriel
I would therefore not consider Nenya to have been jewellery until after the destruction of the one (although whether it was then visible is unclear to me).
She wears Nenya, the Ring of Adamant, one of the Three Elven Rings. It is "like polished gold overlaid with silver light, and a white stone in it twinkled as if the Even-star had come down to rest upon her hand."
She lifted up her white arms, and spread out her hands towards the East in a gesture of rejection and denial. Eärendil, the Evening Star, most beloved of the Elves, shone clear above. So bright was it that the figure of the Elven-lady cast a dim shadow on the ground. Its rays glanced upon a ring about her finger; it glittered like polished gold overlaid with silver light, and a white stone in it twinkled as if the Even-star had come down to rest upon her hand. Frodo gazed at the ring with awe; for suddenly it seemed to him that he understood. 'Yes,' she said, divining his thought, 'it is not permitted to speak of it, and Elrond could not do so. But it cannot be hidden from the Ring-bearer, and one who has seen the Eye. Verily it is in the land of Lórien upon the finger of Galadriel that one of the Three remains. This is Nenya, the Ring of Adamant, and I am its keeper.
Fellowship of the Ring - Book II, Chapter 7: The Mirror of Galadriel
It's not jewelry, but when the Fellowship leaves Lorien,
In the midst of the vessel sat Celeborn, and behind him stood Galadriel, tall and white; a circlet of golden flowers was in her hair, and in her hand she held a harp...
Fellowship of the Ring - Book II, Chapter 8: Farewell to Lorien