Roman Gods, I think, lived where there duties took them. This would be most inline with Italic and Etruscan Gods, who lived in the skies, upon teh earth, under the earth, in the waters. A river god would live in his river, a goddess of the land in her land. The lares and penates lived in the houses or with the families they protected. This has been published widely (e.g. L.B. van der Meer, 1987).
Jupiter, like most Roman deities is most cognate with Etruscan and Italic deities. When the Romans conquered Greece, they found many similarities between their own gods and goddesses and those of the Greeks. 274
The most likely explanation is that many (though not all) of the Greek gods were derived of Etruscan origins, like the Roman gods. Others were from the East, such as Dionysos, and <PERSON>.
It seems unlikely that the Roman pantheon was "infected" with Greek influences, before Greece was conquered, as the only similarities are the ones that likely stem from Etruscan origin. Not a single Greek influence that was of Eastern origin made it into Roman mythology until well after the contacts with Greek colonies in Southern Italy or even the conquest of Greece, which would be statistically most unlikely if the Greeks had "infected" the Roman pantheon before they were conquered.
It would therefore surprise me if Roman Gods lived on Mount Olympos. I think it would be almost impossible for such a notion to have existed in the centuries of Roman mythology before the conquest of Greece, and even after the conquest of Greece, if such a change had happened, one would have assumed there would be explicit mentioning of this. More explicit than <PERSON>'s Hercules Furens.
Even if later in the Roman empire there had been "infection" of Roman religious beliefs by Greek mythology, and even if every single text proving that got lost, does <PERSON> prove anything. In that text <PERSON> never claims any God lives on Olympos. He only says <PERSON> rules Olympos, but in the same play <PERSON> is said to rule several other places as well: the infernal world (line 46-62 and 592-615), the heavens (line 709-730) and all fires (line 926-938). If ruling something means he lives in it, then at the very least <PERSON> lives in many places.
Many Roman deities have epiteths tying them to a place. Perhaps those refer to places where they live? 72