Where did Jesus go and what did he do between His death and resurrection? (non-Trinitarian perspective)

From a biblical literalistic point of view, the answer is very simple.
(TL;DR: it has the same answer as "Where does the light go when you turn off the switch?".)

In the quotations from the King James Bible that follow:

• "Hell" is the Elizabethan English word for "grave", with no supernatural connotations.
• "Soul" is the word for any living creature, even its dead body, with no implications of self-awareness, much less immortality.

As far as I know, this answer represents all denominations that accept those two definitions.

Here are a few of the details provided by the Bible:

• In Matthew 16:21, Jesus explained that he must "be killed, and be raised again the third day".
• In Matthew 12:40, Jesus claimed that he would "be three days and three nights in the heart of the earth".
• In Matthew 26:12, Jesus said that the woman "did it for my burial".
• Ecclesiastes 9:5 says, "For the living know that they shall die: but the dead know not any thing".
• Psalms 146:4 says: "His breath goeth forth, he returneth to his earth; in that very day his thoughts perish.".
• Ezekiel 18:20 says "The soul that sinneth, it shall die.".
• Romans 6:23 confirms this: "For the wages of sin is death".
• Acts 2:31–32 says that David "spake of the resurrection of Christ, that his soul was not left in hell, neither his flesh did see corruption. This Jesus hath God raised up, whereof we all are witnesses.".

So we know that:

• Jesus, was killed and his body buried.
• Like all other humans, his thoughts stopped, his life force disappeared, and the self-aware consciousness of the being known as Jesus ceased to exist.
• Unlike any other human though, he had never sinned, and so hadn't earned that death penalty.
• So God gave Jesus back his life, resurrecting him as his immortal son.

"Where did Jesus go between Death and Resurrection?":

• He went to the grave.

"What did Jesus do between Death and Resurrection?":

• His mind stopped working. He did nothing. As a self-aware being, he didn't exist.

Everything else that over the centuries people have added to the story comes from other, non-biblical sources.

Where did Jesus go and what did he do between His death and resurrection? (non-Trinitarian perspective)

Scriptures tell us that Jesus went to free the spirits in prison. For many this remains a mystery to fully understand.

Peter once of wrote of Paul’s letters: “There are some things in them that are hard to understand” (2 Pet. 3:16). We might say the same of Peter’s letters! Here’s one statement that has long perplexed readers:

For Christ also suffered once for sins, the righteous for the unrighteous, that he might bring us to God, being put to death in the flesh but made alive in the spirit, in which he went and proclaimed to the spirits in prison, because they formerly did not obey, when God’s patience waited in the days of Noah, while the ark was being prepared, in which a few, that is, eight persons, were brought safely through water. (1 Pet. 3:18–20)

Does 1 Peter 3:19 Teach That Jesus Preached in Hell?

Various interpretations have been put forth, so different Churches have different interpretations.

Unitarians, such as Thomas Belsham, considered that the spirits in prison were simply Gentiles in the prison of ignorance to whom Christ preached through his apostles.

The concept that the dead await a general resurrection and judgment either in blessed rest or in suffering after a particular judgement at death was a common 1st century Jewish belief (see Lazarus and Dives and bosom of Abraham). A similar concept is taught in the Eastern Orthodox churches, was championed by John Calvin (who vigorously opposed Luther's doctrine of soul sleep), and is reflected in some Early Church Fathers.

In The Church of Jesus Christ of Latter-day Saints, this verse is used in conjunction with 1 Peter 4:6 to support the belief that in the three days between Christ's death and resurrection, He visited the spirit world and set in motion the work of teaching the gospel to those who didn't receive it during mortality, providing them the opportunity to repent and accept saving ordinances performed on their behalf in Latter-day Saint temples.

Spirits in prison

Qualifications to answer from this perspective: I am a nontrinitarian Christian, monotheist, who believes John 17:3 which teaches that the Father is "the only true God." I also accept that Jesus was a man with flesh and bones (see Luke 24:39) who was possessed by God (see 2 Corinthians 5:19; Proverbs 8:22-31; Hebrews 10:5; John 14:10).

Answer: Jesus was dead from the time of his expiration on the cross to his resurrection, and did not "do" anything nor "go" anywhere. His lifeless body was, of course, removed from the cross and placed in the sepulchre, but of this he would have known nothing (see Ecclesiastes 9:5-6).

During his life, Jesus taught repeatedly that the words he spoke were not his own words, but those of the Father. This is important to understand with relationship to his death because of the prophecy which he had given that...

... Destroy this temple, and in three days I will raise it up. (John 2:19, KJV)

That those were the Father's words is made clear from Acts 13:30:

But God raised him from the dead: (Acts 13:30, KJV)

Jesus, being dead and knowing nothing, could not possibly have raised himself. It was God (the Father) who raised him from the dead, just as it had been the words of the Father which he had spoken regarding his temple.

Jesus confirms the fact that from the time of his death until his resurrection he had not gone to heaven.

¹³And they say unto her, Woman, why weepest thou? She saith unto them, Because they have taken away my LORD, and I know not where they have laid him. ¹⁴And when she had thus said, she turned herself back, and saw Jesus standing, and knew not that it was Jesus. ¹⁵Jesus saith unto her, Woman, why weepest thou? whom seekest thou? She, supposing him to be the gardener, saith unto him, Sir, if thou have borne him hence, tell me where thou hast laid him, and I will take him away. ¹⁶Jesus saith unto her, Mary. She turned herself, and saith unto him, Rabboni; which is to say, Master. ¹⁷Jesus saith unto her, Touch me not; for I am not yet ascended to my Father: but go to my brethren, and say unto them, I ascend unto my Father, and your Father; and to my God, and your God. (John 20:13-17, KJV)

Following his resurrection, Jesus briefly departed to heaven, as he tells Mary, before returning to earth and meeting with the disciples, spending some days with them again before returning to heaven. But all of this happens after he was raised to life; none of this happened between his death and his resurrection.