The text of the Gospel According to Mark does not specifically identify anyone as the author. Not even "Mark" is identified as the author — in theory, "Mark" could have simply related a series of events and stories to someone else who collected them, edited them, and set them down in the gospel form. It wasn't until the second century that the title "According to Mark" or "The Gospel According to Mark" was affixed to this document.
Mark in the New Testament
A number of people in the New Testament — not only Acts but also in the Pauline letters — are named Mark and anyone of them could potentially have been the author behind this gospel. Tradition has it that the Gospel According to Mark was written down by Mark, a companion of Peter, who simply recorded what Peter preached in Rome (1 Peter 5:13) and this person was, in turn, identified with "John Mark" in Acts (12:12,25; 13:5-13; 15:37-39) as well as the "Mark" in Philemon 24, Colossians 4:10, and 2 Timothy 4:1.
It seems unlikely that all of these Marks were the same Mark, much less the author of this gospel. The name "Mark" appears frequently in the Roman empire and there would have been a strong desire to associate this gospel with someone close to Jesus. It was also common in this age to attribute writings to important figures of the past in order to give them more authority.
Papias & Christian Traditions
This is what Christian tradition has handed down, however, and to be fair, it's a tradition that dates back pretty far — to the writings of Eusebius around the year 325. He, in turn, claimed to be relying upon work from an earlier writer, Papias, bishop of Hierapolis, (c. 60-130) who wrote about this around the year 120:
"Mark, having become Peter's interpreter, wrote down accurately whatever he remembered of what was said or done by the Lord, however not in order."
Papias' claims were based upon things he said he heard from a "Presbyter." Eusebius himself is not an entirely trustworthy source, though, and even he had doubts about Papias, a writer who evidently was given to embellishment. Eusebius does imply that Mark died in the 8th year of Nero's reign, which would have been before Peter died — a contradiction to the tradition that Mark wrote down Peter's stories after his death. What does "interpreter" mean in this context? Does Papias note that things were not written "in order" to explain away contradictions with other gospels?
Roman Origins of Mark
Even if Mark did not rely on Peter as a source for his material, there are reasons to argue that Mark wrote while in Rome. For example Clement, who died in 212, and Irenaeus, who died in 202, are two early church leaders who both supported a Roman origin for Mark. Mark calculates time by a Roman method (for example, dividing the night into four watches rather than three), and finally, he has a faulty knowledge of Palestinian geography (5:1, 7:31, 8:10).
Mark's language contains a number of "Latinisms" — loan words from Latin to Greek — which would suggest an audience more comfortable with Latin than in Greek. Some of these Latinisms include (Greek/Latin) 4:27 modios/modius (a measure), 5:9,15: legiôn/legio (legion), 6:37: dênariôn/denarius (a Roman coin), 15:39, 44-45: kenturiôn/centurio (centurion; both Matthew and Luke use ekatontrachês, the equivalent term in Greek).
Jewish Origins of Mark
There is also evidence that the author of Mark may have been Jewish or had a Jewish background. Many scholars argue that the gospel has a Semitic flavor to it, by which they mean that there are Semitic syntactical features occurring in the context of Greek words and sentences. Example of this Semitic "flavor" include verbs located at the beginning of sentences, the widespread use of asyndeta (placing clauses together without conjunctions), and parataxis (joining clauses with the conjunction kai, which means "and").
Many scholars today believe that Mark may have worked in a place like Tyre or Sidon. It's close enough to Galilee to be familiar with its customs and habits, but far enough away that the various fictions he includes wouldn't arouse suspicion and complaint. These cities would also have been consistent with the apparent educational level of the text and seeming familiarity with Christian traditions in Syrian communities.