If you are a tourist in Athens and you dream on Greek islands definitely go there.
Use the Acropolis stop of the metro line, and walk to Anafiotika.
It is like being in Aegean and being in Athens the same time. The view of the city is extraordinary.
You can take some cool photos and enjoy the walk.
As you start going down you will find yourself in Plaka where you can have a coffee, a meal or buy some souvenirs.