Augustus used his rule for the beautification of Rome in order to help sustain and create his image of an all powerful emperor who revitalises Rome and rebuilds it to reflect the glory and power he wanted to show that he had. In my opinion, it was all about projecting and sustaining an image of his own importance and glory.
Augustus also rebuilt many temples. This was to show that he was a traditional person. This was very important, because he was introducing one of the largest changes. He was introducing an empire. Also he wanted to show people that he really did care about the gods. So, he revived religion by his building projects.
One way to go about doing what you're looking for is to look for symbolism in the art. Augustus wanted to do two apparently contradictory things: to project his power while at the same time legitimizing it by referring to Roman tradition. So Romans would have seen different portrayals of Augustus that emphasized his military prowess (he was often depicted in a contrapposto position, holding a spear and wearing a cuirass, or breastplate). These would have resonated with Romans as symbols of military authority and reinforced his claim to power as imperator, or military leader.
But he also sought to connect himself to traditional Roman religion, so you also see him portrayed as pontifex maximus, or the high priest of Rome (a title the Pope would later adopt, incidentally). In this iteration, he was portrayed wearing a toga, with the cloak drawn over his head, and holding religous symbols like sacrificial cups. Other attempts to connect Augustus to Roman tradition included portrayals of him that evoked the legendary Roman founders Romulus and Augustus's supposed ancestor Aeneas. One also sees him portrayed shirtless, with outstretched arm evoking the power of Zeus or Neptune.
These were not just simple exercises in ego, though that was part of it. He was drawing on symbols that resonated with Roman people to legitimize his power.
By commissioning great buildings and art, Augustus made himself look very powerful. He made it look as if his rule caused Rome to be remade. He is famous for having supposedly said that he found Rome as a city of brick and left it a city of marble. This shows what he was trying to do -- he was trying to use the art and architecture to show that he was responsible for a rebirth of Rome.
What I'm looking for is guidance on how to draw different conclusions about what that art and architecture meant during Augustus' reign and how to interpret that evidence?