Ostia

According to Wikipedia, Ostia is "a large neighbourhood in the X Municipio of the comune of Rome ... near the ancient port of Rome, which is now a major archaeological site known as Ostia Antica."

Note that neither Ostia nor Ostia Antica is described as "the [modern] port of Rome".

I have in the past seen Civitavecchia described as the port of Rome. This is (quoting Wikipedia again) "a city and comune of the Metropolitan City of Rome ... a sea port on the Tyrrhenian Sea ... 60 kilometres (37 miles) west–north–west of Rome." It's in the far north–western corner of Lazio, the region of which Rome is the capital.