To the Greeks and later Romans Olympus was the mountain in northern Thessaly. Early Romans did not connect their Gods with Greek counterparts.
Hesiod has Olympus as a mountain
...and the peaks of snowy Olympus resound, and the homes of the immortals
As does Homer in the Iliad...
Down he came, in fury, from the heights of Olympus...
He later describes the Gods as living
...in the fine houses built for them among the folds of Olympus.
The Roman Ovid also describes Olympus as a mountain
I went down from lofty Olympus and, though a god...
Theoi.com has a nice article about Olympos, citing as main source Homer's Iliad.
It was essentially an ancient akropolis--a fortified hill-top and palace complex--located just below the peaks of Mount Olympos. The golden gates of the heavenly fortress were guarded by the three Horai (Horae) and it contained the palace of Zeus, lesser palaces for the other gods, and stables for the immortal horses. The buildings were built of stone with bronze foundations and were surrounded by cloistered courtyards with golden pavements.
The main structure was the palace of Zeus. It had a fairly simple layout--as was typical of ancient Greek palaces--with a central hall, private bedchambers and storage rooms. The golden-floored hall served as both a council chamber and feast-hall for the Olympian gods and provided them an expansive view of the world below allowing them to observe mankind from the heights. The golden tables and tripods of the feast were automatons animated by the divine smith Hephaistos (Hephaestus), and trundled in and out of the hall as required.
Before the palace of Zeus was a large, cloistered courtyard where the full assembly of the gods would gather--including all of the earth-, river- and sea-deities as well as nymphs. The peak of Olympos functioned as the secondary seat or throne of Zeus, apart from the rest of other gods.
The Olympian akropolis lay above the clouds and the paths of the stars, near the apex of the solid bronze-dome of the sky. It existed in the zone known as the aither--the bright upper-air of heaven or shining blue of the sky. The gods feasted on ambrosia and nectar, substances collected from the meadows of the earth-encircling river Okeanos or the smoke of sacrificial offerings wafting to heaven.
Among the most descriptive passages of the Iliad quoted in the article, you can find these:
Afterwards when the light of the flaming sun went under they went away each one to sleep in his home where for each one the far-renowned strong-handed Hephaistos had built a house by means of his craftsmanship and cunning. Zeus the Olympian and lord of the lightning went to his own bed, where always he lay when sweet sleep came on him. Going up the bed he slept and Hera of the gold throne (khrysothronos) beside him.
Homer, Iliad 1. 493 ff
The pressure held their heads on a line [the Greek soldiers], and they whirled and fought like wolves, and Eris (Hate), the Lady of Sorrow, was gladdened to watch them. She alone of all the immortals (theoi) attended this action but the other immortals were not there, but sat quietly remote and apart in their palaces (dômata), where for each one of them a house had been built in splendour along the folds of Olympos.
Homer, Iliad 11.72 ff
She went into her chamber, which her beloved son Hephaistos had built for her, and closed the leaves in the door-posts snugly with a secret door-bar, and no other of the gods could open it. There entering she drew shut the leaves of the shining door, then first from her adorable body washed away all stains with ambrosia, and next anointed herself with ambrosial sweet olive oil, which stood there in its fragrance beside her, and from which, stirred in the house of Zeus by the golden pavement, a fragrance was shaken forever forth, on earth and in heaven.
Homer, Iliad 14.153 & 14.225 ff
The same quotes can be found in the English edition of the Iliad at the Perseus site, but in some cases they have different number citations: Hom. Il. 1.493, Hom. Il. 11.47, Hom. Il. 14.154.
The Odyssey doesn't seem to add much, except that the weather there was quite fine:
So saying, the goddess, flashing-eyed Athena, departed to Olympus, where, they say, is the abode of the gods that stands fast forever. Neither is it shaken by winds nor ever wet with rain, nor does snow fall upon it, but the air is outspread clear and cloudless, and over it hovers a radiant whiteness. Therein the blessed gods are glad all their days, and thither went the flashing-eyed one, when she had spoken all her word to the maiden.
