Athens, a big ugly city, has obligatory ancient sights (the hilltop temple of the Acropolis, and the ruined forum of the Agora); an extremely touristy old quarter (the Plaka); and fine museums — the best in the country. Its four million people sprawl where no tourist ventures, including new immigrant zones with poor yet thriving communities. The joy of Greece is outside of Athens. See it and scram.
Delphi is a touristy little mountain resort with a breathtaking, mountainous setting. It's a long way to drive (three hours from Athens) for some ancient ruins. But learning about the oracle (whom the ancients consulted for advice) and being there in the empty cool of the early evening, you know why, in ancient times, this was considered the center of the world.
