Is this the Elostirion?

Question

In this clip at the very beginning in the first seconds there are towers seen high up the hill.

Are they or one of them intended to be the White Towers or do they belong to the Grey Havens already? I guess if anything, the one in the image above is, namely the Elostirion as that is the only of the White Towers from which you can see the sea. Do we know how close the Elostirion is to Mithlond?

Answer 1

In the prologue to The Lord of the Rings, we read:

For the Elves of the High Kindred had not yet forsaken Middle-earth, and they dwelt still at that time at the Grey Havens away to the west, and in other places within reach of the Shire. Three Elf-towers of immemorial age were still to be seen on the Tower Hills beyond the western marches. They shone far off in the moonlight. The tallest was furthest away, standing alone upon a green mound. The Hobbits of the Westfarthing said that one could see the Sea from the top of that tower; but no Hobbit had ever been known to climb it.

and in the final chapter:

And when they had passed from the Shire, going about the south skirts of the White Downs, they came to the Far Downs, and to the Towers, and looked on the distant Sea; and so they rode down at last to Mithlond, to the Grey Havens in the long firth of Lune.

In The Silmarillion (Of the Rings of Power and the Third Age):

At Fornost upon the North Downs also the Númenóreans dwelt, and in Cardolan, and in the hills of Rhudaur; and towers they raised upon Emyn Beraid and upon Amon Sûl; and there remain many barrows and ruined works in those places, but the towers of Emyn Beraid still look towards the sea.
It is said that the towers of Emyn Beraid were not built indeed by the Exiles of Númenor, but were raised by Gil-galad for Elendil, his friend; and the Seeing Stone of Emyn Beraid was set in Elostirion, the tallest of the towers. Thither Elendil would repair, and thence he would gaze out over the sundering seas, when the yearning of exile was upon him; and it is believed that thus he would at whiles see far away even the Tower of Avallónë upon Eressëa, where the Masterstone abode, and yet abides.

I would say that the structures in the video are not these towers.

• They are too close to the Grey Havens and to the sea. Not long after reaching the Towers you should be able to see the "distant Sea", whereas in the video it is very near. (It could be that it means the open sea beyond the firth, however.)
• It also feels like the Towers are not in the environs of the Havens themselves. The sense is that they are between the Shire and the Havens, but not part of either. Appendix A(I)(iii) mentions briefly that "the Tower on Emyn Beraid that looks towards the Gulf of Lune" held a palantír that was "guarded by the Elves". That sounds more like the Elves of the Havens took responsibility for the Towers, as they were nearby, rather than that they were already part of the Havens proper. Unfinished Tales concurs that they "were maintained and guarded by Círdan and the Elves of Lindon" (note 16 to Part IV, Chapter III).
• Politically, it appears that although the Towers were raised by Gil-galad, High King of the Noldor, they were part of a larger Númenórean settlement (now represented by "barrows and ruined works"). While Gil-galad had the authority to build near or within the Havens, as he was also the king of Lindon in particular, it sounds more like the exiles setting up independently, and then being graced by a special architectural gift. I would think that like the other places mentioned, this was in previously unclaimed land: a part of the North-kingdom and not of Lindon.
• From "standing alone on a green mound" I get the impression that the Tower Hills are topographically more like the Downs (which are low rolling hills). In the video it is quite a bit more mountainous and rugged, not really a "green mound". The terrain here is more reminiscent of the breaking of the Ered Luin after the fall of Thangorodrim, which is when the gulf was formed - a rupture in the mountain range, happening to create a good harbour.
• Sam's daughter Elanor later lives "at Undertowers on the Tower Hills" (year 1462 S.R. in Appendix B). That is twenty years before Sam himself passes through the Havens. This land was adjoined to the Shire by Aragorn, and many Hobbits moved there. Again, it feels like it's not right next to the Havens, and that the remaining Elves there probably didn't have immediate Hobbit-neighbours.