This is a great question, because there is an understanding that art and architecture is a means to show political power and other messages. In fact, the images on the coins that the Romans used were probably the most effective way to spread messages and ideas. In view of all these points, let me show how Augustus' reign used art and architecture.
First, Augustus obviously used architecture to show how great he was. For example, he boasted in the Res Gestae that he left Rome a city of marble. In other words, he made the city of Romebeautiful beyond measure through his reign.
Second, he also communicated that he was a restorer of religion. In other words, through his restoration of temples, he tried to show the Romans that he was a very traditional emperor. Here is a small quote from the Res Gestae.
"I built the senate-house and the Chalcidicum which adjoins it and the temple of Apollo on the Palatine with porticos, the temple of divine Julius, the Lupercal, the portico at the Flaminian circus, which I allowed to be called by the name Octavian, after he who had earlier built in the same place, the state box at the great circus, the temple on the Capitoline of Jupiter Subduer and Jupiter Thunderer, the temple of Quirinus, the temples of Minerva and Queen Juno and Jupiter Liberator on the Aventine, the temple of the Lares at the top of the holy street, the temple of the gods of the Penates on the Velian, the temple of Youth, and the temple of the Great Mother on the Palatine."
Finally, through art, another point that Augustus showed was his tolerance. He allowed many poets like Ovid, Vergil, and Horace at times to write things that were not always flattering to him.
In short, through art and architecture, Augustus was able to communicate many different messages.