The Isle of Patmos is a very small Greek island in the Aegean Sea. About the place where the author John writes there is little debate; the same is not true about the author of the Book of Revelation, the last book of both the New Testament and the Bible. Most believe that the John who writes this vision of Armageddon and the End Times is the same John who was a disciple of Jesus Christ. This John wrote the Epistle John as well as I, II, and III John. Some modern scholars suggest that this is some other John, not one of Jesus' disciples. In any case, we know enough about him to determine who his audience is.
The first two verses explain that John is writing the vision that God gave him, and in verse four we begin to learn the answer to your question:
4 John to the seven churches which are in Asia: Grace be unto you, and peace, from him which is, and which was, and which is to come; 6 ...And hath made us kings and priests unto God and his Father; to him be glory and dominion for ever and ever. Amen....
Verse four specifically addresses this writing to seven churches in Asia Minor (modern-day Turkey); more generally, in verse nine, John makes it clear he is writing to fellow believers, fellow Christians.
I John, who also am your brother, and companion in tribulation, and in the kingdom and patience of Jesus Christ, was in the isle that is called Patmos, for the word of God, and for the testimony of Jesus Christ.
In the days following Jesus' Crucifixion and Resurrection, the Christian church begins and then grows; however, it is not free from persecution. In fact, Christians are under heavy persecution after Jesus is gone, as evidenced by the fact that nearly all of His disciples were martyred for their faith. So, when John says he is their "brother" and their "companion in tribulation," it is clear he is referring to fellow believers and followers of Christ's teachings.
Because Revelation is visionary and symbolic, it is open to many interpretations. The seven churches are both literal and symbolic, as noted in several of the links attached below. The seven physical churches to whom John wrote are these:
The seven churches to which the letters were addressed were Ephesus, Smyrna, Pergamos, Thyatira, Sardis, Philadelphia, and Laodicea. These cities stood along one of the ancient postal Roman roads of that day, and, beginning at Ephesus, would have been visited in the order in which they are named. The distance between each is about 50 kilometres; a full day's journey on foot.
It is in verse three, however, that we get the more general audience for which John intended these words:
3 Blessed is the one who reads the words of this prophecy, and blessed are those who hear it and take to heart what is written in it, because the time is near.
While John addresses his words specifically to the believers in seven churches, his broader audience is anyone who will one day read or hear his words and take them to heart. This makes sense, as this apocalyptic book is a prophetic warning about things that will come to pass in the last days before things on earth will change forever and Jesus will return to reign on earth.
John is actually speaking to the church and believers of Christ. While in the island of Patmos stranded and alone God gives him a revelation about what is to come for us. This book is describing the times that we are living in the 21st century when the bible was written thousands of years ago.