Disembarking in Athens - Why Not Do Santorini?

My wife and I are taking a cruise from Italy to Greece, stopping in Crete, Mykonos, and landing in Athens. We've always liked the idea of experiencing Santorini (white buildings, views, swim out pools, etc) so we thought we would spend a few days there, but understand it's one of the more expensive islands. We're not big shoppers or party people, but love our wine and cocktails while meeting locals. We really just want the "pool/lacuzzi overlooking the ocean" vibe - any alternatives we should look into?

I'm looking into Anemomilos and Amorgos, but open to all the input!