After the War of Wrath the world is changed and Beleriand is sunk into
the see. Only a small strip called Lindon remains of what had been Ossiriand,
west of the Ered Luin. It is there that most Noldor and Sindar settle down,
with Gil-Galad as their king.
Elrond is Gil-Galad's master-at-arms, and Círdan establishes the Grey Havens at
After a while Galadriel and Celeborn depart from Lindon to abide
Galadriel probably visits back to Lindon around the occasion of the visit of Tar-Aldarion of Numenor around the 7th century. For she receives from Gil-Galad the mallorn seeds given to him by the King of Westernesse.
It is around this time that Galadriel hears rumors of evil shadows reawakening in the east. Then she and Celeborn move to inspect the seriousness of the threat and move eastward. From time to time we see them in Eregion, where Celebrimbor starts his Noldorin settlement of craftsmen, sometimes even east of the Misty Mountains, in the land east of Khazad-dûm then called Lorinand, and beyond, to the north and south.
In Eregion the Noldor establish great friendship with the dwarves of Khazad-dûm. Together they create marvels of art and technique, as is shown in the doors of Moria. It has been told that in these days Celebrimbor succeeded in recreating the Elessar, the elvenstone which he had made in Gondolin but was lost, and that he gave the new Elessar to Galadriel.
Then it came to pass that when Annatar, Lord of Gifts, came to Eregion pretending to be an emissary of Aulë, sent by him to enhance further their already illustrious achievements, he is welcomed by many. But not by Galadriel, who does not trust him, and warns Celebrimbor against him. But not even Galadriel perceives at that time the true identity of the Giftlord.
Since her warnings go unheeded Galadriel moves eastward again, to the
It is told in many stories what then came to pass, between the 15th and 17th century SA. The rings of power were forged, and also - in secret, for Celebrimbor still had the words of Galadriel in his ears - the three Elven-rings. And then at last Celebrimbor perceives his error. The true identity of Annatar is revealed as none other than Sauron, remaining lieutenant of Morgoth, who by some scheme or fate had escaped the onslaught of Angband. But then it is too late, for already Sauron has succeeded in creating the master-ring, The One Ring to rule all others. Many Lords of Westernesse - wearing the Nine - become his minions. Many Lords of Dwarves - wearing the Seven - become imprisoned. And nigh all that elves, men and dwarves had created in those great centuries was laid bare to Sauron, Lord of the Rings.
Thus starts the war between Sauron and the elves of Eregion, in which at last Eregion is destroyed and Celebrimbor slain. But before his death Celebrimbor seeks out Galadriel to ask advice what to do with the three Elven-rings, unspoiled by Sauron. And while Nenya is given directly to Galadriel, Narya and Vilya are sent to Gil-Galad in Lindon.
Many years later, before going to battle with Sauron in the Last Alliance, Gil-Galad - having the gift of high-elves to foresee his ending - gives Narya the Red to Círdan of the Grey Havens, and Vilya the Blue to his lieutenant Elrond. But Nenya the White still is where it has been: with Galadriel. And thus it was at it should be: for these were the noblest of elves left in Middle-earth.
We cannot be quite sure where Galadriel and Celeborn abode during the many years between the fall of Eregion (around 1700) and the end (3441) of the Second Age that came with the demise of Sauron and the death of Gil-Galad and Elendil. But it is certain they still did not take any dominion of their own. Galadriel felt it as her mission to unite the free peoples against Sauron and to this end she visited many courts and places. But she had learned deeply from the history of her people, and the Prophecy of the North was in her veins: not by her fighting directly could evil ever be defeated. So she worked in secret, in the background, helping many, dominating nobody.
 A fact which might raise questions. Why - for instance - not Galadriel, who was the sole survivor of the earlier generations? The explanation is that the high-kingship would follow the family trees. First in line was the tree of Fëanor, who was eldest son, thus high-king after Finwë. When Maedhros refused his rights (and other sons of Fëanor by their actions were disqualified), the position went to Fingolfin, second son, who was succeeded by his sons Fingon and after his death Turgon. After the sack of Gondolin the title passes by right to Fingon's son Gil-Galad.
Note that if Maedhros would not have refused his rights, then Celebrimbor would have been high-king at the start of the 2nd Age. Note as well, that by these rulings, Elrond as a descendant of Turgon would have had legitimate rights to the high-kingship in the 3rd Age. But Elrond refused any such claim.
 This little known fact is told in A Description of the Land of Numenor, Unfinished Tales, p. 217. Lothlorien is the only place in Middle-earth where the mallorn - originally existing in Aman - would grow, but that is later, well into the 3rd Age, when Galadriel starts making full use of her powers.
 In other tales the Elessar was given to Galadriel by Olorin/Gandalf, Unfinished Tales, pp. 321-326.
 In another variant of the story Galadriel and Celeborn are actually the rulers of Eregion, and only go east after its destruction.
These travels between Eregion and the land later known as Lothlorien were - undoubtedly - a bit of a torture for Celeborn, who had to travel the long way around the south of Enedwaith. For he would always refuse to follow his wife into Khazad-dûm, by his dislike of the dwarves who slew his kin.
 This is my interpretation of her motives. See "Third Age" next for further references.