A few comments after a recent trip.
I cannot discourage enough renting a car in Athens. There are many good suggestions here for private cars for your touring and all the official guides in Greece are certified. Delphi was amazing (it's a good amount of walking). The drive alone was interesting and pretty. The recent NYT article on Athens has pinpointed the new emerging spot for dining in Athens. The concierge at the GB had good suggestions as well.
The GB was terrific. I'd probably use FHR or Virtuouso to get a slightly better room confirmed.