What sort of maps did the ancient Greeks make and distribute?

Just because nothing survives of early cartographic works does not mean they did not exist. In History we often have to gather information from earlier historical writings, discussing earlier works yet. Gathering information on Geography, and recording this information, Cartography, predate Ptolemy by hundreds of years.

Early Cartographers and Geographers

A section of the wiki page for Anaximander 610-546 BC,

Both Strabo and Agathemerus (later Greek geographers) claim that, according to the geographer Eratosthenes, Anaximander was the first to publish a map of the world. The map probably inspired the Greek historian Hecataeus of Miletus to draw a more accurate version. Strabo viewed both as the first geographers after Homer.

Maps were produced in ancient times, also notably in Egypt, Lydia, the Middle East, and Babylon. Only some small examples survived until today. The unique example of a world map comes from late Babylonian tablet BM 92687 later than 9th century BC but is based probably on a much older map. These maps indicated directions, roads, towns, borders, and geological features. Anaximander's innovation was to represent the entire inhabited land known to the ancient Greeks.

The Babylonian map of the World (6th Century BC) also illustrates that the concept of cartography was alive and well in the 6th Century BCE.

Geographic texts:

Hecataeus of Miletus(c. 550 BC – c. 476 BC) was slightly later, and is said to have improved upon Anaximanders work. Another publication of his however, the Periodos ges, may give you a clue to the level of cartographic knowledge attainable by the ancient Greeks:

Periodos ges was written in two books, the first on Europe, the second on Asia, in which he included Africa. The book is a comprehensive work on geography beginning at the Straits of Gibraltar and going clockwise ending at the Atlantic coast of Morocco following the coast of the Mediterranean and Black Sea. Hecataeaus provides information about the people and places that would be encountered on a coastal voyage between these points, as well as the inhabitants of the various Mediterranean islands, the Scythians, Persia, India, Egypt and Nubia. Over 300 fragments of this work are preserved, mostly as citations for place names in the work of Stephanus of Byzantium.6

Though a written work and not a map per se, this indicates that geographical information for the creation of maps was at hand. This tradition is maintained in nautical circles at least, with the production of the periplus

A periplus (/ˈpɛrɪplʌs/) or periplous is a manuscript document that lists the ports and coastal landmarks, in order and with approximate intervening distances, that the captain of a vessel could expect to find along a shore.

Later, by Roman times (I know off topic for your question) this concept was modified for inland use along roads as the Roman Itinerarium:

...was an Ancient Roman road map in the form of a listing of cities, villages (vici) and other stops, with the intervening distances.

So we can see the concept of cartography was available for your ancient Greek era RPG, at least from the 6th Century BCE. The fact that written works describing the geography of a region existed meant that someone could interpret this data in the form of a map. The information was being gathered and interpreted by the scholars of the time, the philosophers and geographers and historians.

Implied existence and availability of early maps

The remaining question would be how commonly would you encounter these maps. One particular example demonstrates the (limited) public availability of maps. From the History of Cartography, volume 1, chapter 8, pg 139 (emphasis mine):

A story in Aelian of Socrates and his rich pupil Alcibiades shows that any Athenian could consult a world map. Seeing Alcibiades blinded by wealth and boasting of his big estates, Socrates took him to a place in the city (Athens) where a world map [pinakion, diminutive of pinaxl was set up. He told Alcibiades to look for Attica; and when he had found it, he told him to look carefully at his own fields. Alcibiades replied: "But they are not drawn in anywhere." Socrates: "Why then, you are boasting of fields which are not even a part of the earth.

Another example from the same page in the History of Cartography, (also mentioned in comments), is a humorous discussion from a fifth-century comedy by Aristophanes, The Clouds, which takes place in a classroom type situation, where a student is pointing out the location of various cites on a map on the wall, and the observer recommends moving Sparta farther away.

These demonstrate the availability of maps, at least at an institutional level. (The exception might be for nautical type charts or coastal maps in seaport type areas)

So we know maps were available, but possibly scarce. If you did find such maps,the accuracy was rarely expressed in absolute terms, but mainly in positional knowledge. The most accurate information would come from the most commonly traveled routes, such as shorelines and rivers.