Right this is a pig of a question for a few reasons. Firstly do you mean within the urbanised metropolis of Rome, Constantinople(which really has a direct continuum right into and across the medieval period until its sack) or other large cities? Secondly do you mean culturally , technologically or militarily advanced? and thirdly what dates are you giving to the 'middle ages'. Because that goes all the way from padded armour to gothic full plate and cannons?

Your emphasis on Rome at its peak is problematic as the seat of the empire changes, by the end of the western Roman empire Rome isn't even the main city in Italy(I believe that falls to Revena?) let alone the empire. At any rate please ask a more specific question or a few and I will try to answer.