Well that depends on what period of time you are talking about. During the period from the Gracchi through the end of the civil war between Antony and Octavian, the turmoil was largely in the city itself. You have figures like the tribunes of the plebs Clodius and Milo who using their own supporter, former gladiators, and street thugs would try to keep the areas where assemblies or voting might take place free of opposition (A Roman magistrate could only conduct the duties of their office in person, so if you kept you opponent from showing up, he couldn't veto or otherwise perform his duties). The politics of the late republic and in effect control of the whole empire at times hinged upon who had the most thugs in the forum at the time.

During the Principate the turmoil in the provinces could manifest in the streets of Rome, news of the Teutoburg Forest disaster could cause riots of panic in the city. During the 250-ish years between the Principate and the crisis of the 3rd century Most of the Emperors resided mainly in Rome and didn't leave it very often. Tiberius on Capri, Trajan's campaigns, Hadrian's travels, and Marcus Aurelius' Germanic Wars are really some of the most prolonged times the Emperors weren't in Rome (I have omitted more instances, but the point is that Rome was usually where the emperor would be found.) Think too when Nero committed suicide, most of the empire still supported him, and had he run to the east to rally support he could likely have crushed Galba, the Senate, and Praetorians who were against him.