That is a good question. The people in that area spoke Attic Greek. We are lucky to have many authors who have preserved Attic Greek. In fact, you can learn it at almost any college. It is usually called classical Greek as opposed to Hellenistic Greek, which was used after the death of Alexander, and Koine Greek, which is the Greek of the Bible (New Testament). Some authors that wrote in Classical or Attic Greek are: Sophocles, Plato, and Demosthenes. I highly recommend that study of Attic Greek. It will expand your and broaden your mind.
The Athenians spoke what was called Attic Greek. This dialect was spoken in the entire region around Athens.