I forgot what special I was watching, but it was going over the history of the Roman emperors. One historian said it was kind of an unwritten rule that Roman emperors must build something big and new in Rome during their reign. Nowhere in that special did they mention special projects in London, Paris, or even Constantinople. When I thought about it, I realized there aren't any special structures in those cities on the scale of Rome's projects. Am I wrong, or did Rome just not care about other major cities?
Engineering feats were commonly held as a testament to Rome's power, a way to showcase (in some functional ways such as Aqueducts, or non functional ways such as the Pantheon) the might of Rome, the accomplishments of Rome. For this reason, it was always a popular move with the people to build something new or undertake a big public work.
To add, many of the infrastructure projects in Rome were driven by a large populace. At the height of the Empire, Rome's population was around one million, and that is an absolutely staggering number for ancient city center at the time. Also, Rome was such a center of commerce and consumption, we also would want to take into account all the traders and merchants that would come through from other parts of the empire, sure to take stories home of whatever new marvel had been built in Rome. So if you wanted something to be seen to project Roman Power and influence, actually building it in Rome is a pretty good way to make sure it gets noticed by the most people.
With that said, there are some really great Roman Architectural ruins outside of Rome, perhaps less densely found as opposed to what is found around Rome, but nonetheless Roman and still standing..Parts of them anyway! They show style and flair, and well laid out cities despite being so far away from the capitol.
The Leptis Magna Arch in Libya
The Amphitheater at Aspendos in Turkey
The Amphitheater in El-Djem Tunisia
The Capitol at Dougga, Tunisia
Palace remains of Thermes de Constantine in Arles, France
The temple and columns in Baalbek Lebanon
The ruins at Djemila Algeria
The Basilica of Volubius in Morocco
Timgad Ruins in Algeria
The Theater Ruins at Apamea Syria
The Ruins at Jerash Libya
The Ruins at Conimbriga Portugal
Well while the most visible momuments of the Roman empire remain in Rome, there were still plenty of massive building projects that were undertaken across the Roman world. Of course they did not just plop down massive building projects in any old city and because of Rome's centrality to the Empire, until very late in its existence,
Some of the more famous projects would be Hardian's Wall, the rebuilding of Carthage into a Roman City, and Constinople and Ravenna turned into Imperial cities almost overnight and received th ebuilding projects one would expect to go with it. Constantinople comes immediately to mind with the Theodosian Walls, the palaces, and later on the building projects of emperors such as Justinian I and the Hagia Sophia rivaled anything ever built in Rome itself.
For further reading I'd suggest taking a look at John Bryan Ward-Perkins's Roman Imperial Architecture or Karen Ros's article in the American Journal of Archaeology for a specific example and analysis of a theater in Carthage (year 1996).
For projects in Constantinople I would recommend Cyril Mango's Byzantine Architecture