Today's Athens consists of 2 cities, Ancient Athens and Modern Athens. There is very little left in between and those surviving structures that are, are called "neo-classic" or consist mostly of Byzantine religious structures.
Unlike the cities of Paris, Berlin, Madrid, Prague, London, Vienna, St. Petersburg and Rome, few grand, medieval or imperialist-era spawned structures exist in Athens unless you want to count the Acropolis. The Turks certainly didn't build any that survived.
Ancient Athens, was put out of business in the 4th Century AD, by the Christian Emperor Theodosius, based in Constantinople capitol of Byzantium. He banned all pagan worship and closed the famous Schools of Philosophy. Christian zealots smashed many priceless artworks during this period as well. Athens lay fallow for centuries.
Through-out the 400 year Turkish occupation and until about 1830 Athens consisted of only 6,000 souls or less, mostly clustered in dwellings clinging to the slopes of the Acropolis and today's Agora, Plaka and Monastiraki areas. Its Greek Orthodox residents had over 100 churches within the city limits whose total area was about 160 acres. (The Greek unit of property measure is the "strema" and equal to 1/4 acre)
When the Turks were finally ousted from Athens and the Acropolis, archeologists removed and destroyed everything which dated later than the classical period from the site.
The destruction of the Frankish Tower is the most glaring example. This famous landmark was a legacy from the Crusader occupation of Athens and the last place where the sacred owls of Athena nested. It should have re-erected elsewhere but wasn't The power vacuum created by the ousting of the Ottoman Empire by heroic Greek resistance and with the undeniable help of the Great Powers was filled by the imposition of a foreign monarchy in 1830.
Their funds combined with those of wealthy diaspora Greeks created the nucleus of the cities modern center: The Royal Palace (now the Parliament), Syntagma Square (Constitution Sq.), Omonia Square (Concorde Sq.) and the few roads linking them contain Athens larger and most imposing structures most identified with a European style capital.
These include the Academy or University, the National Library, the Old Parliament (now the National History Museum) the Arsakion (an 1836 girls school turned court building) and German born Philhellene Henrich Schleimanns' (father of Modern Archeology) old mansion (now the Numismatic Museum). The National Gardens & the Zappion Building derive from this era as well.
Additionally the real old quarter of Athens, except for a single church, which stood on the site of the current ancient agoras, was razed to the ground by American archeologists after World War II in order to expose the foundations and drainage system of the buildings of the classical period.