I think that the Palantír could see to the Tower of Elostirion on Tol Eressëa, where it is said the "Master Stone" was kept. The answer is definitely in Unfinished Tales.
I think the White Towers were mainly built as watchtowers, like the one on Amon Sűl/Weathertop. Probably there were only ever a few people living there at any time. Maybe they worked on rotation, sometimes living in the cities of Arnor, in the same way that Gondor kept watchers on the beacon hills. The White Towers sound nice though, don't they?
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But Gwindor answered: 'The doom lies in yourself, not in your name'.
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