The only mention of a palace in Númenor that I'm aware of is that in Armenelos, the capital, which occurs in Description of the Island of Númenor in Unfinished Tales:
...the summit of the tower of the King's palace in Armenelos...
As for other great buildings, Aldarion and Erendis (also Unfinished Tales) mentions Vëantur's house:
That house had its own quay, to which many small boats were always moored, for Vëantur would never journey by land if he could by water...
We can assume that a house with its own quay large enough for "many small boats" is sufficiently great to meet the requirement. This also suggests that Lords of Númenor did maintain great houses.
Elendil's house is also described in the first Númenorean chapter of the Lost Road (HoME 5) in terms that also seem to meet the requirement:
Elendil was walking in his garden, but not to look upon its beauty in the evening light. He was troubled and his mind was turned inward. His house with its white tower and golden roof glowed behind him in the sunset...
And:
...his eyes rose by chance to his own house among trees and flowers upon the slopes above the shore, white and golden, shining in the sunset...
Although not a king, Elendil can therefore be said to have certainly lived in a "great building", at least one of a somewhat lesser scale than a palace.