One small quibble: it sounds as if you are talking about "artifacts", that is, the work of human (or other) hands; "relics", at least in our world, is a word more usually associated with religious
objects, specifically the remains of saints, especially their bones. It's perhaps a slight difference, but useful, I think; if we consider the terms that way, we see, for instance, that there does appear to be a certain reverence toward tombs, at least of the great -- the Hallows in Rath Dinen,
Balin's tomb in
Moria -- but not, as far as I can tell, a feeling that these remains contained an inherent power, certainly not in the same way they have been regarded in "our" world -- by the religious, I mean.
On the other hand, the Oaths of Cirion and
Eorl took place before the tomb of
Elendil, and even after its removal, the hill was either revered or feared, or both, by the
Rohirrim, and called by them the Halifirien -- "Holy Mountain" -- so there may be more to it than
Tolkien described.
Archeologically, there must have been a number of
ruins, far more than are seen in the story. We do get some glimpses of these; someone, I think Alcuin, suggested that the hill in Hollin where the Fellowship fought the
wargs was the site of
Celebrimbor's Hall. I don't know, but from the description, I'd prefer to think it may have predated the coming of the
Noldor. A "broken circle of boulder-stones" sounds "prehistoric" to me, anyway.
As for artifacts,
the one which has most fascinated and puzzled me over the years is the Stone of Erech: why on
Middle Earth would someone go to the trouble of transporting a 12-14 foot diameter stone all the way from
Numenor, only to set it up, basically in the middle of nowhere? Tolkien moved its location, and changed its purpose, several times, but the final result still leaves unanswered questions. It remains -- for me, at least -- one of the most mysterious objects in Middle Earth.