I would recommend you start with a few of his contemporaries, just to see what others were saying at the same time he was writing. People like Jerome, Possidius and Orosius being a few I can tick off the top of my head.

Also to put his time period into perspective, I'd look into controversies around his time, such as the Easter Confrontation between Ambrose and Empress Justina in AD 386, and the Slaughter of Thessalonika in AD 390 (for primary sources, check out CT 9.40.13 and Rufinus HE 12.18). And if you want to have a bit of perspective as to what occurred not long after Augustine, look into the likes of Benedict of Nursia (AD 480-547). And a little earlier into the issue of the Nicean Creed in AD 325 (be brief with that though. Just get a quick summary -- you don't want to bog yourself down, but you should know a wee bit about the Arians vs Nicaeans just to put the concerns of Augustine into context).

Augustine was a prolific writer, so getting through his opus is a daunting feat. The sources I've listed just now were to put his theological concerns into perspective, but in order to get the full effect of De Civitate Dei, you also might want to look into the Germanic invasions resulting in the sack of Rome in AD 410. For that you'll want to look into how Theodosius dealt with the Goths, and the complicated relationship between Stilicho and Alaric after Theodosius' death in AD 395. For that, unfortunately, you'll have to wade into the murky waters of Zosimus Historia Nova. Be careful with him; he's a character.

Again, these are all primary sources. If anyone else would like to add a few more to this list, or to add some secondary sources, by all means.