That's an interesting question. Some notable options:
Constantinople. It was the capital of the Roman Empire for about as long as Rome (Rome- 753 B.C. to 455 A.D.= 1208 years (fungible on either side), Constantinople- 330 A.D. to 1453 = 1123 years). It was one of the great centers of learning, and as the center of the quintessential bureaucracy (source of the term "byzantine"), it produced a lot of documents that can tell us about the inner workings of the government. Downside- conquered by forces that were in some ways hostile to that history, so less access to all of that knowledge; it was also in many ways closer to an Eastern, or Greek kingdom, very different from the Western, Roman, state.
Pompeii (and Herculaneum). It was frozen in time right during the golden age of Rome. It can provide an awful lot of information about that one specific age, which also happens to be (roughly) the most well documented and studied part of the Roman Empire. Downsides - A lot of the stuff we'd hope for is pretty well damaged by, you know, the volcano. The early excavations were done by people that would have horrified modern archaeologists. It only provides a glimpse into a brief sliver of an empire that, depending on how you count, lasted up to 2000 years.
3...) You could also make cases for a few other cities like Alexandria (Egypt) and Athens (obviously it was independent during the Greek golden age, but it was under Roman/Byzantine rule for roughly 1500 years), and a few others.
I'm sure you'll get other answers of European Roman cities but Palmyra is a well studied city in Syria. It's not roman in origin, but when it was incorporated into the Roman Empire it prospered. I'd recommend looking it up because it tells us a lot about how Roman religion was incorporated into the indigenous Semitic religions of Syria. They worshipped Canaanite gods like Baal but there were also roman, Babylonian, and other cults. It was in the news recently because ISIS captured and we will unfortunately most likely lose some of its history to their iconoclasm. It's an interesting city to read about if you want to know more about how Rome affected the middle Eastern societies it annexed.