If I recall correctly, some family (the Crescenti or the Frangipani, I can't recall) fortified the Colosseum during the bloody disputes for the Papal chair in the 10th Century. For people who can't grasp how huge the amphiteatre is: those aristocrats managed to build a citadel inside it... using the walls as curtain walls

Also, I believe that the Island on the Tiber (
Isola Tiberina) was fortified due to its significant strategical position inside the city of Rome.
Also, to the OP think its useful to point out that the Gothic War of the 6th Century resulted in the destruction of most of the acqueducts that provided water for the citizens. As the flow of water coming from the mountains was not actually impeded, the fluvial discharge accumulated for centuries produced some rather expansive swamps inside the Roman town, and diseases brought by mosquitos (mainly malaria, already presente in Italy since Ancient Era) were a very serious concern, so much that some Popes would invest resources in the draining of the wetlands.
If I recall correctly, the area around the Vatican - which in the context of Ancient Rome is located in a suburban area - grew in population as the importance of the Papacy rose in the High Middle Ages, and after the building of the Leonine Wall in the 9th Century.