To really appreciate Athens you would need to spend at least a week. At least a day to see the Acropolis and the Parthenon. Another day or two to see the fascinating National Archaeological Museum of Athens. Furthermore, during the summer season the Athens festival is held at the Theater of Herodes Atticus under the rock of the Acropolis and is the ultimate opportunity to see on stage an ancient Greek drama.
During the Athens Festival, there are many world famous artists who perform at the ancient theater. It is an amazing experience on a warm evening to watch a display on that great Amphitheatre.
Next to the Parliament the National Garden and the Zappeion are places of interest a green oasis in the middle of the big city, walking through Zappeion you arrive opposite the Panathinaikon Stadium where the first modern Olympics took place in 1896.
A few metres away towards the Acropolis you have the monuments of the ancient temple of Olympic Zeus and the Adrianos Gate, at this point starts the Adrianou street which takes you through Plaka all the way down to Monastiraki with its flea market and Thission.
From Arios Pagos you can watch the Sound and Light displays which are held every summer in Athens at the Pnika hill. The sound and light show consists of light and sound effects on the Acropolis and the Parthenon. The Lycabetous Hill is another place of interest something like the hill of Sacre Coeur in Paris. Though the tiny church of St George on the hill doesn't have the status of the Parisian church, the view is worth seeing, especially the ascent of going up in the same kind of funicular train like in Paris. But the heart of Athens for the tourist and many Greeks as well, is the areas of Plaka Psiri and Monastiraki.