Tricky to define 'important'
The problem with picking Rome is that you are really referring to the Roman Empire, and that's not the same thing as the city. Whilst the Empire started there,. Rome itself actually ended up being of very secondary importance. It was declining as the major city of the Empire from AD onwards and a couple of centuries in saw half a dozen other places in the Empire being far more significant than the ill-placed, cut off over-fed bunch of temples that was Rome. The last place any of the later Emperors ever really spent any time in was Rome.
Most notably, Constantinople was a much greater city than Rome ever was, as far as the ways you can rate the importance of a city in an Empire was concerned. It was on a major land and sea trade route, it provided enormous amounts of money, it became the centre of the Roman Empire (eclipsing Rome entirely), outlasted its western cousin by a thousand years, and was the richest city in Europe for most of its history. A much better candidate for 'miost important city' than Rome ever was.
Rome provided nothing. All it did was suck food out of the Empire. It was not strategically important nor did it produce anything worthwhile.
Compare again, for example, London- access to the ocean and centre of both political and economic power; esseential to the whole regime.