Christ’s soul and spirit undoubtedly went directly into the presence of the Father. This is suggested by the fact that (1) His work on the cross paid the full price for our redemption; His substitutionary work was finished, and (2) by the fact that He told the thief, “Today you will be with me in paradise,” a reference to the abode of the righteous dead and which may be a synonym for heaven.
However, that does not mean that His spirit might not also, having first gone into heaven, then proceeded to tartarus where He made a glorious proclamation of his finished victory to those demonic spirits who had been bound in tartarus. They could not have know that Christ had sealed their destiny of judgment by His victory on the cross. Remember, Gen 3 anticipated Satan’s doom and that of his demonic hosts, but some were bound in pits of darkness to wait their final judgment—a judgment based on the victory by the Seed of the woman. This defeat of Satan and his forces is an important aspect accomplished by the cross (see Col. 2:15). This involves a great deal of other issues involving not only 1 Peter 3:18-19, but also Genesis 6, Jude, and 2 Peter 2:4-10.
For a good study on this, see the lesson on Genesis 6 in Bob Deffinbaugh’s series, Genesis: From Paradise to Patriarchs on our web site.
Of course, some believe the 1 Peter 3 passage refers not to Christ’s spirit, but to the Holy Spirit’s ministry in the days of Noah.