Octavian remained away from Rome after Actium, and entered into his fifth consulship in absentia. He had major issues to sort out, even after the defeat of Antony, and while we don't know the specifics, we know the general outline: he had to reorganize the administration of Egypt as a Roman province so that the much-needed grain could be extracted from there and sent back to Rome, the urban population of which was burgeoning. Octavian was a savvy politician and always knew that the urban plebs had to be appeased, in this case with renewed grain shipments after the relatively recent chaos. Second, he had to see to the disbanding of a positively massive armed force, dozens of legions from both sides, all of whom expected to receive the same retirements as their spoiled predecessors had received. Both Antony and Octavian had made many promises. By the time this task was finished, over a hundred thousand soldiers would be settled in veteran colonies all over the Mediterranean, from Provence to Tunisia to the Near East to Greece.

Third, he had to see to the Eastern provinces, get them re-re-re-re-organized (after Sulla, then Lucullus, then Pompey, then Antony), and politely receive envoys from probably three dozen cities. Some of them wanted to worship him as a god, as was their Hellenistic tradition. He decided that the Roman citizens there would have temples to Roma + Divine Iulius; the non-Romans would have Roma + Divine Octavian (later Augustus)(so Dio says anyway: 51.20.6-9).

He returned to Italia in the Summer of 29 and celebrated a triple-triumph for Dalmatia, Egypt, and [edit: Actium]. His young proteges Marcellus and Tiberius Claudius Nero rode with him in the parades. He was there to preside over the opening of the new senate house, the Curia Iulia, and to see his adopted father's new forum inaugurated with the Temple of the Divine Julius. Other than that, he probably hung out with Agrippa, Vergil, and Maecenas and listened to a lot of Latin poetry.

Early in the next year, 28, Octavian was consul again, of course, but we also find him and his right-hand-man Agrippa being awarded censoria potestas, the right to act as if censors. With this, they performed the ritual lustrum, a purification of the city, the first one since Pompey and Crassus had done the same as co-consuls way back in 70 BCE in an attempt to clear the bad air of Sulla's reign of terror. They also used their censoria potestas to purge the ranks of the senate. In 28 are the first "Actian" games, and also the completion of the shiny new temple of Apollo on the Palatine Hill (now taking shape as the future Imperial palace). In 28 he also announced that at the end of the year, the special powers of the triumvirs (only him left, of course) would expire. That sets us up for the show in January of 27.

In 27, Octavian and Agrippa were joint consuls (Octavian's 7th). In January of 27, in a famous speech of the senate, Octavian apparently "handed back" the reins of the Republic to the Senate. He did not, of course, not really. It was the carefully-orchestrated "settlement"

Most of this you can get from Dio's histories, or from Suetonius. You are right that things were relatively quiet, especially before Octavian had returned. The decisions about imperial cult, settlement of soldiers, and the organization of Egypt were momentous in retrospect, but probably expedient at the time. Some of the actions of this time period are a little lackluster on paper, but very important in the moment. The lustrum is a good example, or the completion of that temple of Apollo, both of which had powerful symbolic value as far as Rome's future and Octavian's place in that future.