When you arrive at the “Eleftherios Venizelos” Athens international airport and are waiting for your flight to Santorini, there is not enough time to visit the city of Athens. The airport is an hour’s drive or train ride.
Instead of hanging out at the airport, you could go to the Sofitel Hotel, which is exactly opposite the airport door (at a distance of 50 meters). There is a nice coffee area indoors and outdoors. I propose you spend your free time between the flights there.
Transportation in Santorini
The only public transportation in Santorini is the quite efficient local bus system. It is easy to learn and to feel comfortable using it. It should be noted thought that busses stop at midnight every night of the week (except from the weekends in the busiest summer months), so visitors should to plan their return accordingly.
The main bus station is located in Fira near the main square. It should be noted that there are no busses which run directly from one side of Santorini to the other so visitors who expect to travel to both sides of Santorini will likely become very familiar with the main bus station which is where major bus transfers will occur. There are seven main bus routes used by tourists. More information is available in Ktel Santorini.