"Within" is translated from entos, used only twice in the New Testament. Its primary meaning is "inside," as it is rendered in Matthew 23:26: "Blind Pharisee, first cleanse the inside of the cup and dish, that the outside of them may be clean also." However, when used in conjunction with a plural noun, entos means "among" or "in the midst of." In Luke 17:21, entos is used with "you," and from the context, we can see that Jesus was speaking to a crowd of Pharisees, who had come to question Him about the Kingdom of God (verse 20). "You," then, is plural. "The kingdom of God is among you" is best.
Most modern translations have recognized this grammatical error and translate entos as "among" or "in the midst of." Some texts, like the New King James and the New International versions, persist in using "within," though they note in the margin that "among" is an alternative.
Even without this technical knowledge of Greek, we could have easily understood that "within" is a poor and misleading translation. Christ was answering a question posed by the Pharisees, and He replied directly to them: "He answered them and said, . . . 'For indeed, the kingdom of God is within you.'" But how could the Kingdom of God be within His most bitter enemies? How many times did He reveal them to be hypocritical and misleading the people? Theologically, it is quite impossible to think that His Kingdom would be in the Pharisees.
It is only after He had made this remark that He turned to His disciples (verse 22) and explained what He meant. The subject of the entire section (verses 20-37) is stated most explicitly in verse 30: "Even so will it be in the day when the Son of Man is revealed." All along, He had been explaining His second coming! When He returns, He will set up His Kingdom on earth (Zechariah 14:9).
If the Kingdom is still future, how could He say that "the kingdom of God is among you"? To answer this, we must return to the four common traits of a kingdom: a king, who rules by law over a number of subjects who live within a certain territory. The primary trait is that a kingdom must be ruled by a king; otherwise, the country has some other form of government. A king of any nation is the chief representative of that nation. And the King of the Kingdom of God is none other than the living Jesus Christ!
Pilate specifically asked Jesus, "'Are You a king then?' Jesus answered, 'You say rightly that I am a king. For this cause I was born, and for this cause I have come into the world, that I should bear witness to the truth'" (John 18:37). So as the King of God's Kingdom, He could truly tell the Pharisees that the Kingdom of God was among them.