We know from Jesus' statement to the thief that when one dies they enter the presence of God immediately. Luke 23:42 states, "Truly I say to you, today you shall be with Me in Paradise." This statement also tells us that Jesus went to His Father upon death.
Beyond this we know very little about where Jesus was for three days. One must be careful not to read too much detail into a parable or story. The issue in Jesus recounting the story of Jonah was to relate to His anticipated three days of being dead. Reading Jonah 2:2, some translations say "from the depth of Sheol", another translation says "from the depth of hell", still another says "from the grave." What is clear is that that Jonah assumed he was a dead man inside the fish as he prayed.
Later, in Jonah 2:6 we are told his "life was brought up from the pit." Some interpreters assume that this is a reference to hell. However, a very simple interpretation of the Bible takes this as a reference to death, the imagery is the grave. Sheol is not hell; to the Hebrew mind it is death; a place where the soul waits for resurrection and judgment. The context of Jonah 2:6 is "the earth with its bars was around me forever." He is using imagery to say he felt just the same as if his body was buried in the earth (grave) and he was locked there forever.
There are other passages that are used to suggest that Jesus went to hell during the three days His body was in the tomb. If one wants to believe that He went to hell, then the verses can suggest it. However, if the verses are simply taken one-by-one, they do not support that belief