If you look for maps you'll quickly note that all the maps showing the empire at its greatest extent will say 117 CE on them. That's the death of Trajan, who conducted the last large expansions of the empire. He conquered Dacia (north of the Danube), Nabatea (SE of Jerusalem), Armenia, and Mesopotamia (along the Eastern borders). He decisively beat the last big state accessible to Rome (Parthia) and occupied their capital Ctesiphon. His son Hadrian decided that the Eastern border left Rome vulnerable and withdrew from much of Armenia and Mesopotamia. So the empire at its height is easy, it was 117 CE.

The city is a more interesting, but likely has an answer around the same time. Trajan was the second in a line that was known as "The Five Good Emperors." These were five emperors who ruled from 96 CE to 180 CE. And have long been considered the golden age for the Empire and City. All were long ruling. All were considered good administrators. All were civic minded and Trajan and Hadrian especially were considered great builders and civic planners. Several of the last great buildings were during this time. And the city probably reached its max population in the early to mid second century.