Where and how did Roman civilization develop?

It developed in Rome. The Romans were Latins and shared the culture of the other Latin cities. It was said that Rome was a fusion between Latins and Sabines who settled there, so there was, at the beginning some influence from these neighbours who leaved on the mountains to the east. Their Etruscan neighbours also had an influence in the early days. By far the biggest influence was by the Greeks. The Romans were fascinated by their myths, copied their architecture adopted some of the Greek gods and associated their own divinities to Greek ones. They looked up to the Greeks and the elites spoke Greek. Thus Roman civilisation developed through a mixture of Latin culture and outside influences. These outside influences increased when the empire expanded and the Romans got in contact with more cultures.
it developed in central Italy and spread across the empire.