As you begin to explore, you may find it helpful to look up to the Acropolis, west of Syntagma Square, and to Mount Likavitos (Lycabettus), to the northeast. From most parts of the city, you can see both the Acropolis and Likavitos, whose marble lower slopes give way to pine trees and a summit crowned with a small white church.
Think of central Athens as an almost perfect equilateral triangle, with its points at Syntagma (Constitution) Square, Omonia (Harmony) Square, and Monastiraki (Little Monastery) Square, near the Acropolis. The area bounded by Syntagma, Omonia, and Monastiraki squares is defined as the commercial center, from which cars are banned except for several cross streets. At one time Omonia Square -- Athens's commercial hub -- was considered the city center, but nowadays, most Greeks think of it as Syntagma Square, site of the House of Parliament. The two squares are connected by parallel streets, Stadiou and Panepistimiou, and where you will find the Neoclassical University Trilogy. (Panepistimiou is also known as Eleftheriou Venizelou.)
Flanking the Parliament building is one of Athens's most beautiful parks, the National Gardens. Right adjacent is the Zappeio Hall and gardens, another beautiful oasis in the center of the city. West of Syntagma Square, Ermou and Mitropoleos lead slightly downhill to Monastiraki Square, home of the city's famous flea market. From Monastiraki Square, Athinas leads north back to Omonia past the modern Central Market. The old warehouse district of Psirri -- now the home of many chic galleries, cafes, and restaurants -- is between Athinas and Ermou.
If you stand in Monastiraki Square and look south, you'll see the Acropolis. At its foot are the Ancient Agora (Market) and the Plaka, Athens's oldest neighborhood, many of whose street names honor Greek heroes from either classical antiquity or the Greek War of Independence. The twisting labyrinth of streets in the Plaka can challenge even the best navigators. Don't panic: The Plaka is small enough that you can't go far astray, and its side streets with small houses and neighborhood churches are so charming that you won't mind being lost. An excellent map may help. Also, many Athenians speak some English, and almost all are helpful to direction-seeking strangers -- unless you happen to be the 10th person in as many minutes to ask where the Acropolis is when it is clearly visible!
Finding an Address -- If possible, have the address you want written out in Greek so you can show it to your taxi driver, or ask for help from pedestrians. Most street signs are given both in Greek and a transliteration, which is a great help. Most taxi drivers carry a good Athens street guide and can usually find any destination. Increasingly, however, some Athenian cabbies are newcomers themselves to the capital and may have trouble with out-of-the-way addresses.
Street Maps -- The free maps handed out at branches of the Greek National Tourism Organization have small print and poor-quality paper. You may prefer to stop at a newspaper kiosk or bookstore to pick up a copy of the Greek Archaeological Service's Historical Map of Athens (with maps of the Plaka and of the city center showing the major archaeological sites). The map costs about 4€.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.