When in Athens, visit one of the world-famous Greek islands for a day or two. Simply book your ferry boat ticket for Aegina which you'll receive in your email. With your e-ticket, go to the harbor of Piraeus, a 30 min metro ride from downtown Athens and board one of the boats.
Choose one of the main departure times and a 1-way or 2-way boat transfer ticket. Aegina was the first capital of the modern Greek country in the 19th century and its main town is considered a cosmopolitan in the summer and charming in the winter.
On the island, you'll find both organized and untouched human beaches, as well as majestic mansions, ancient Greek temples, arts, culture, and nightlife. There are wonderful mountain hikes for nature lovers and scenic villages with local-made delicacies and traditions.
Give Aegina a couple of days more than you originally planned. It will happily surprise you and make you want to return, time and again.