After Satan's fall from heaven, why did God put Satan on earth in Paradise with Adam and Eve instead of another part of the universe without life?
God banished Satan and all the evil angels to hell after they rebelled against him (2 Peter 2:4; Jude 6). In his wisdom, God allows the fallen angels and their leader to roam the earth (Job 1:7; 2:2; 1 Peter 5:8). In his wisdom, God allowed Satan to tempt Eve in the Garden of Eden—as you noted.
In the Bible, God does not explain his actions, nor does he need to (Romans 11:33-36). What the Bible does teach is that God controls Satan’s activities (Revelation 20:3), and the day is coming when Satan and all the evil angels will be confined to hell forever (Revelation 20:10). That ultimate confinement will take place because Jesus successfully carried out his mission of destroying the devil’s work (1 John 3:8).