What is the Biblical basis against the omnipresence of Satan? Many Christians pray and act as if Satan is right next to them all the time, tempting them to turn away from God, attacking them, etc., as though he were omnipresent...

What is the Biblical basis against Satan's omnipresence?
After some study, I can conclude that there is no biblical evidence for Satan being omnipresent.

God is omnipresent

in the sense that where ever we go, He is there:


  Psalm 139:7-8
  Where shall I go, away from Your Spirit, And where shall I flee from Your presence? If I ascend into heaven, You are there; If I make my bed in Sheol, there You are.


And also in the sense that He fills all in all:


  Ephesians 1:22-23 "And He subjected all things under His feet, and gave Him to be the head over all things to the church, Which is His body, the fulness of the One who fills all in all."




Satan is not omnipresent

Satan, on the other hand, is cast out of heaven in Revelation 12, showing he has a physical presence which can be limited:


  Revelation 12:7   And there was war in heaven: Michael and his angels went to war with the dragon. And the dragon warred and his angels.
  
  12:8   And they did not prevail, neither was their place found any longer in heaven.
  
  12:9   And the great dragon was cast down, the ancient serpent, he who is called the Devil and Satan, he who deceives the whole inhabited earth; he was cast to the earth, and his angels were cast down with him.


The Bible also never says that Satan fills all things, but only that he can enter specific people for a purpose, the same as all evil spirits:


  Luke 22:3-4   And Satan entered into Judas who was called Iscariot and was of the number of the twelve. And he went away and conferred with the chief priests and officers as to how he might deliver Him up to them.
  
  Acts 5:3   But Peter said, Ananias, why has Satan filled your heart to deceive the Holy Spirit and to put aside for yourself some of the proceeds of the land?