In OTL modern Greece was founded by Greek intellectuals influenced by the French Revolution, and were abetted by Phil-Hellenic Western Europeans enamored by the legacy of classical Greece, including Lord Byron. This meant that instead of drawing its legitimacy from the Eastern Roman Empire (i.e. the last Greek independent polity), the then Kingdom of Greece drew it more from classical Greek polities, hence the capital of Athens.
So what other scenarios for Greek independence would be plausible, and what would their effects be culturally and politically?