This needs a bit of an explanation, and please, bear with me:
Will any person living be exempt from seeing the Second Coming of Jesus? I guess, the answer should be - "no", because the Second Coming can be understood not only in a sense that He will come in the End of the human history, in eschatology, but that every living human being will face Him and come to His judgment after death. This meeting with the Lord will in no way be any less intense and dreadful than that of those people who will live in the final stage of history and perceive physically Jesus' coming to the earth. For everybody will come to the judgment of Christ, or judgment seat of God (Romans 14:10-12), which is the same, and the passed away people will stand before this judgment seat immediately after death. In fact, we even during the life stand before this judgment seat, but often hush it or turn blind eye to it and continue our sinful ways, yet after death we shall be deprived of this opportunity and the judgment seat will shine before us: for the unrepented sinners in a painful way, for the righteous in a joyful way.
The same, seemingly "false prophesy" is expressed with this regard in the words of Jesus "I tell you, this generation will not pass away until all of these will take place" (meaning in "all of these" the events of the Second Coming) (Matthew 24:34). But "that generation" passed away and historical Second Coming did not happen. So what? Did Jesus say a lie? A blasphemy even to think this! But what He in fact meant was that all intensity of war of good and evil, Christ and Antichrist in human hearts will happen in all generations with the same intensity as in the end of history. Thus, a Christian persecuted by, say, Lenin (bolsheviks, as a matter of fact, killed at least 300 000 clerics not to mention millions of simple believers) is no less experiencing the blows of evil than a Christian persecuted in the times of Antichrist; and also, the first, Lenin-time Christian will be crowned with the crown of glory for the forbearance and martyrdom not of a lesser brilliance than a similar Christian in the time of the last persecutions by Antichrist. So, sorry future Christians of the time of the Antichrist, - you will not have any privilege above any generation that has lived before you, for all generations will participate in a fight against powers of evil with not a tiny bit lesser intensity than you! And this is the meaning of Christ's saying that "this generation will not pass until all of this will take place", and this saying, thus, applies to all generations before the end of history.
This is the key to understand your passage as well: how many cities were there in Israel? Quite a few (I have counted almost 50 of them). I guess, the number is big enough to make it impossible for a single persecuted individual to traverse all of them during a lifetime: just imagine, how long it would have taken to authorities to spot a suspicious person at that time? Probably, at least several months and even years. The saying is the same as when Jesus tells to Peter, "forgive not seven times per day, but seventy times seven per day" (Matthew 18:22), meaning that Peter should always be ready and always in duty of forgiving, for it is impossible that any person wrongs you seventy times seven per single day. Similarly, in the case of the cities, Jesus simply says that Christians will be persecuted their entire lives and come to His judgment seat, as if He said: "Being Christians and thus My followers, you will be hated by the world and persecuted; search not persecutions, provoke them not, but the persecutions will nevertheless come, for you are not of this world; and until the end of your lives, i.e. until my Second Coming - for you will come to My full presence after passage from the historical life to eternity - harbour no illusion that you may find a calm place on earth where the persecutions can end - there is no such place on earth! - but only in heaven eternal glory awaits to those who overcomes (cf. Revelation 3:5)".
To sum it up: it is not a false prophesy, but a way of explaining to His followers that there will not be a rest on earth for His followers for entire of their lives and that they should always be ready to suffer for Him, for all will experience His Second Coming, either in the sense of coming to His presence after death or in the sense of also physically seeing Him at the end of the human history.