Days 1-3 — Athens Core
Follow the 3-Day Athens Itinerary as your base: Acropolis and its museum on day one, central Athens (Syntagma, National Garden, Monastiraki) on day two, a single day-trip choice (Cape Sounion or a Saronic island) on day three.
Days 4-5 — An Island Overnight, Not Just a Day Trip
This is the real upgrade a week buys you: instead of a rushed same-day return, take the ferry to Hydra or Aegina and stay one or two nights. Hydra in particular changes completely once the day-trip crowds leave on the afternoon boats — car-free streets, donkeys instead of traffic, and a much quieter pace.
Days 6-7 — Delphi or Deeper Athens
Either head to Delphi for an overnight (the ancient site is genuinely worth more than the rushed half-day version most day-trippers get), or stay in Athens and explore Kolonaki, Koukaki and the food scene at an unhurried pace — see Athens Neighborhoods and Athens Food & Dining for where to go.
The single biggest advantage of 7 days over 3 is trading a rushed island day trip for an actual overnight — that alone changes Athens from a checklist city into a place with real breathing room.