Vague memories that they "visited" grandma
Galadriel in
Lothlórien, though whether that was before
Aragorn and the four
Hobbits managed to reach
Rivendell or after, before the Fellowship of nine left it - memory fails.
Elladan and Elrohir did visit
Lórien on behalf of their father: from “
The Ring Goes South” in
The Fellowship of the Ring,
they … made a great journey, passing down the Silverlode into a strange country, but of their errand they would not speak to any save to
Elrond.
Now the same passage indicates that other scouts also passed over the Dimrill Stair, but it does not describe their activities other than searching for
servants of Sauron, the
Ringwraiths in particular. The “strange country” is clearly Lórien, I believe.
In “Lothlórien”,
Haldir tells
Legolas and
Frodo when he first meets them that
“[T]he messengers of Elrond passed by Lórien on their way home up the Dimrill Stair.
Haldir is clearly not informed about the Ring or any other of the concerns of
the Wise, but his statement would seem to indicate that he thinks Elladan and Elrohir, “the messengers of Elrond”, traveled beyond Lórien: I suspect that instead they stayed many days with
Celeborn and Galadriel, relating what they knew of Frodo’s flight and pursuit, what had transpired between
Saruman and
Gandalf, all the other debates and information exchanged at the
Council of Elrond, and everything else they had learned in Rivendell; and Celeborn and Galadriel then told them what they knew, and they received the counsel of the their grandparents to give to their father. Since Elladan and Elrohir “would not speak [of their errand] to any save to Elrond,” it is not surprising that Haldir knows nothing of this, and may have mistaken the long delay between their coming to Lórien and leaving as an indication that they visited some other destination.
I, too, have wondered who might have been sent out by Elrond to confront the
Nazgûl south and north of Rivendell. In the essay “
Glorfindel” in
Peoples of Middle-earth,
Tolkien writes,
[Glorfindel] was one (the most powerful, it would seem) of those sent out from Rivendell when the disquieting news reached Elrond that Gandalf had never reappeared to guide or protect the
Ring-bearer.
But as far as I know, he never describes whom else was sent out from Rivendell, whether alone or in small groups.
Just read in many meetings [fotr] "elladan and Ellohr were away on errantry" during the dinner but it seems with the
rangers of the north attacking
orcs as they often did because of their mother. However enough time was passed that they might have gone after frodo and returned, only to leave once more. But I think it might support what was said by
Squint-eyed Southerner
I think so, too. Elladan and Elrohir were clearly entrusted by Elrond with his innermost thoughts and concerns in their visit to Celeborn and Galadriel, and were deep in his councils. They had returned out of the wild the evening Frodo awoke: Aragorn tells us that when
Bilbo asks him why he was not at the feast. It stands to reason that besides Glorfindel and Erestor, Elrond’s chief counsellor, Elladan and Elrohir also attended the Council of Elrond.
It’s off topic, but I strongly suspect that although Tolkien disclaims knowing what became of them, Elladan and Elrohir, like their sister
Arwen, elected to remain in Middle-earth after Elrond left.