After trawling through related questions on Christianity Stack I found a link to a Catholic website that provided the following information on what happened to these apostles:
Saint Peter – Catholic Information:
The New Testament says nothing about Peter's life after his presence at the meeting in Jerusalem with James and Paul (Acts 15). Later sources say that Peter went to Rome, was martyred (64-68) under Nero, and buried on Vatican Hill. Evidence concerning his presence, activity, and death in Rome is slight. He took part in the deliberations of the council in Jerusalem (Acts 15:1-31; Gal. 2:1-10) regarding the relation of the Gentiles to the church. This subject had awakened new interest at Antioch, and for its settlement was referred to the council of the apostles and elders at Jerusalem. Here Paul and Peter met again. We have no further mention of Peter in the Acts of the Apostles... After this he appears to have carried the gospel to the east, and to have laboured for a while at Babylon, on the Euphrates (1 Pet. 5:13). There is no satisfactory evidence that he was ever at Rome. Where or when he died is not certainly known. Probably he died between A.D. 64 and 67. Source: http://mb-soft.com/believe/txh/peters.htm
St. Paul - Catholic Information:
After 2 years in prison he used his right as a Roman citizen to appeal to the emperor and was sent to Rome for trial. The Book of Acts ends with Paul under house arrest (c.63), still preaching about Jesus... Ancient tradition makes it possible to establish the following points: Paul suffered martyrdom near Rome at a place called Aquae Salviae (now Tre Fontane), somewhat east of the Ostian Way, about two miles from the splendid Basilica of San Paolo fuori le mura which marks his burial place. The martyrdom took place towards the end of the reign of Nero, in the twelfth year (St. Epiphanius), the thirteenth (Euthalius), or the fourteenth (St. Jerome). According to the most common opinion, Paul suffered in the same year and on the same day as Peter; several Latin Fathers contend that it was on the same day but not in the same year; the oldest witness, St. Dionysius the Corinthian, says only kata ton auton kairon, which may be translated "at the same time" or "about the same time". Source: http://mb-soft.com/believe/txo/paul.htm
St. John the Evangelist - Catholic Information:
He suffered under persecution, and was banished to Patmos (1:9); whence he again returned to Ephesus, where he died, probably about A.D. 98, having outlived all or nearly all the friends and companions even of his maturer years. There are many interesting traditions regarding John during his residence at Ephesus, but these cannot claim the character of historical truth. With Eusebius (Hist. eccl., III, xiii, 1) and others we are obliged to place the Apostle's banishment to Patmos in the reign of the Emperor Domitian (81-96). Previous to this, according to Tertullian's testimony (De praescript., xxxvi), John had been thrown into a cauldron of boiling oil before the Porta Latina at Rome without suffering injury. After Domitian's death the Apostle returned to Ephesus during the reign of Trajan, and at Ephesus he died about A.D. 100 at a great age... On the other hand the stories told in the apocryphal Acts of John, which appeared as early as the second century, are unhistorical invention. Source: http://mb-soft.com/believe/txn/john4.htm
St. Andrew - Catholic Information:
According to a popular but mistaken tradition, Andrew was crucified on an X-shaped cross. The crossed bars of the Scottish flag are derived from this belief. St. Andrew is the patron saint of Scotland and Russia. It is generally agreed that he was crucified by order of the Roman Governor, Aegeas or Aegeates, at Patrae in Achaia, and that he was bound, not nailed, to the cross, in order to prolong his sufferings. The cross on which he suffered is commonly held to have been the decussate cross, now known as St. Andrew's, though the evidence for this view seems to be no older than the fourteenth century. His martyrdom took place during the reign of Nero, on 30 November, A.D. 60); and both the Latin and Greek Churches keep 30 November as his feast. Source: http://mb-soft.com/believe/txh/andrew5.htm
St. Thomas the Apostle - Catholic Information:
Eusebius of Caesarea records that Thomas became a missionary to Parthia. The Acts of Thomas (3d century), however, states that he was martyred in India. The Malabar Christians claim that their church was founded by him. This tradition can neither be substantiated nor denied on the basis of current evidence. Saint Thomas' Mount in Madras is the traditional site of his martyrdom.
St. Thomas - Coptic Orthodox Information:
Tradition records that Thomas traveled to the east and spread the gospel through Parthia, Persia and India. One tradition has the Savior appearing to Thomas and sending him to India. To get there he hired himself as a slave to an Indian merchant and sailed to India. There he entered the service of King Gondophares. In India he met his death near Bombay, where he was martyred. Death came via a spear or lance which was stabbed through his body while he was kneeling in prayer. Source: http://mb-soft.com/believe/txh/thomas5.htm
I am pleased to have found this source and I trust it is in order to partially quote from it in order to share this information.