Minas Tirith

[Gwaihir the Windlord]

Now in their debate some had counselled that Minas Morgul should first be assailed; and that if it might be taken, should be utterly destroyed. [The Black Gate Opens, RotK]

Minas Morgul had been totally corrupted and ruined, methinks, and would probably -- although no longer a threat upon Gondor, as it was unmanned -- have had to have been demolished. The valley it lay in had been utterly defiled by blackness and evil; 'the evil that lay upon that vale...', so that I doubt it could have in any way been reclaimed.

A more interesting question is that of Osgiliath. It, unlike Minas Morgul, was presumably still rebuildable. I would have thought that the King Elessar would undertake to raise it up from its ruins, the once-mighty city, although still keeping Minas Tirith -- I suppose it really had become, irriversably, a Tower of Guard rather than a mere 'Tower of the Sun' -- suitably as his already long-established capital.

Re Minas Tirith being the centre of the King's united-Numenorean kingdom power; this would make sense, although Arthedain was still the capital of the North (perhaps in the same way that Edinborough, to use a modern example, is capital of Scotland under London), as Gondor would always be the stronger of the two domains.