Athens (and the wider region of Attica) is a city where you can literally find and do everything. Wonderful beaches are almost everywhere. There, besides swimming, you can enjoy your favorite water sports. Yet, if the surface of the sea is not enough for you, you can dive and explore the beautiful seabed.
If you are a mountain-type, fear not. Beautiful high mountains surround Athens (Parnitha, Hymettus), inviting you to enjoy hiking and climbing. If walking is too exhausting or you simply want something different, Attica has a plethora of riding clubs, where you can ride a horse.
If organized entertainment is your thing, you will also find several options here. Vast amusement parks and water parks for all ages. Fields for any sport you like, from football and basketball (the Greek favorites) up to golf. If you are the extreme type, Attica has kart racing tracks where you can reach incredible speeds, having as rival either the timer or your friends, and Paintball fields ready to shelter memorable battles.
In short, Athens and Attica have many suggestions in different regions, you just decide what you prefer!