I know a lot of people are confused between flying and taking the ferry to the islands (we were too). But there are persuasive reasons for taking the ferry.
That evening we pretty much just walked around the Plaka area. Its quaint cobbled streets are lined with restaurants. The streets take you around the Acropolis Museum, Hadrian's Arch, the Roman Agora, the Ancient Agora of Athens, and the Acropolis itself.
I took to researching about Greece like a moth to a flame. It became my favorite pastime; by the time we were ready to leave for Greece, I felt I knew our destinations - Athens, Mykonos, and Santorini - inside out!