Acts 3:19 appears to be alluding to Deuteronomy 30:1 and Deuteronomy 30:1 appears to be predicting Acts 3:19. But let's not miss the forest for the trees.
First of all, the question asks, "To what are we to return" but "we" are not in the equation. He is speaking to Jews, not to Christians:
[Act 3:12 KJV] 12 And when Peter saw [it], he answered unto the people, Ye men of Israel, why marvel ye at this? or why look ye so earnestly on us, as though by our own power or holiness we had made this man to walk?
So he elaborates on their denial of the Lord's anointed one:
[Act 3:13-18 KJV] 13 The God of Abraham, and of Isaac, and of Jacob, the God of our fathers, hath glorified his Son Jesus; whom ye delivered up, and denied him in the presence of Pilate, when he was determined to let [him] go. 14 But ye denied the Holy One and the Just, and desired a murderer to be granted unto you; 15 And killed the Prince of life, whom God hath raised from the dead; whereof we are witnesses. 16 And his name through faith in his name hath made this man strong, whom ye see and know: yea, the faith which is by him hath given him this perfect soundness in the presence of you all. 17 And now, brethren, I wot that through ignorance ye did [it], as [did] also your rulers. 18 But those things, which God before had shewed by the mouth of all his prophets, that Christ should suffer, he hath so fulfilled.
So when he says "Repent ye therefore" he is saying, "I just showed you how guilty you are of rejecting your messiah, so now you need to do the opposite...":
KJV Acts 3:19 Repent ye therefore, and be converted, that your sins may be blotted out, when the times of refreshing shall come from the presence of the Lord;
But this is all pre-Pauline. God had not yet revealed to Paul the seven secrets and the gospel of the grace of God. He is referring to the time of the Jews' visitation. It seems to me that a visitation is a targeted judgment. There was a day coming very shortly (70AD) when:
KJV Matthew 3:12 “His winnowing fan is in His hand, and He will thoroughly clean out His threshing floor, and gather His wheat into the barn; but He will burn up the chaff with unquenchable fire.”
The temple would be city would be destroyed, including the temple. A third of the Jews of Jerusalem were killed, while the Christians obediently fled the city and survived.
So it would be in the judgment of that day that it would be decided by judgment who would enter the kingdom of God and who would be incinerated.
The "times of refreshing" refer to the bliss of the messianic age and the revitalization of all things.
In the Pauline dispensation (the current age) once someone believes they are immediately translated into God's kingdom:
KJV Colossians 1:13 Who hath delivered us from the power of darkness, and hath translated us into the kingdom of his dear Son:
Sin is immediately forgiven and not counted hence.
In summary, the Jews were being called upon to turn from their rejection of their messiah to embracing him.