How were these writings influenced by Augustine's own personal experience and the historical context?

Augustine of Hippo is thought to have completed this work in 426 AD. In order to understand how his own experiences and context drove him to write this book, we must first appreciate what a radical change had just taken place in the balance of power in Europe.
The eponymous "City of God" refers to the heavenly kingdom of New Jerusalem to which good Christians look forward, but Augustine's work is also very much concerned with the Earthly City, or the City of Man, as personified by Rome. For centuries, Rome had dominated the Western world; its empire had stretched far beyond Europe; the Roman way of life had been imposed upon countries from Africa to Britain, and the Empire had begun to seem indefatigable. In 410 AD, however—sixteen years before Augustine completed this book—the unthinkable happened: Rome fell to the Vandals. The rest of its Empire, too, was being eroded over the decade just before Augustine wrote this text, as the Franks took Gaul and the Anglo-Saxons took Britain. The days of Rome were over, a fact which seemed so incredible that it prompted the Romans to wonder which God or gods were responsible and what they had done to offend them.
Rome in the early fifth century was divided by religion; although Constantine in the early fourth century had decriminalized Christianity and the religion had begun to dominate, there were many in Rome who still adhered to the old ways. Following the fall of Rome, traditional Roman pagans accused the nascent Christian religion of destroying their city, angering the Roman gods, and eliciting the destruction of the empire. They also asked how, if the Christian God was so powerful, he had failed to protect the city. It was in response to this argument that Augustine wrote The City of God: it directly addresses the accusations from Roman pagans that the spread of Christianity across the Empire had occasioned it to fall.
Augustine's ultimate thesis is that although what had happened to Rome was terrible, to say it was caused by Christianity was to ignore the fact that bad things had happened to Rome in the past during the days of the pagan gods. He says that the lengthy endurance of Rome is evidence of the true God at work, rewarding ancient Romans for their faith and good behavior even when they were not aware of Him. (This question of achieving the City of God through "works" rather than "faith" is one that would be discussed many times and cause much splintering in the Christian religion in the centuries to follow, but Augustine makes clear that paganism itself could be condoned so long as the people were virtuous—implying that contemporary Roman pagans were not.)
Effectively, Augustine's text provides a rebuttal to the Roman pagans who blamed Christianity for the fall of Rome while also presenting them with an alternative to the Eternal City in the form of the City of God, which promises eternity of a better kind to those who might be willing to become Christians.