Visible from the heights of the Acropolis are the near reaches of the Saronic Gulf and its islands of Salamis (5 minutes) and Aegina (1hr) with Hydra, Poros and Spetses (5hrs) close behind.
Salamis, the very closest island to Athens is historically important because in ancient times, the Athenian navy, under Themistokles, defeated the Persian, under Xerxes, in the worlds first recorded naval encounter.
The island is not suitable for most tourists due to the industrial activities nearby. Aegina and the other islands of the gulf are however, and each is different in its way.
Aegina is so close that some people commute to Athens or Piraeus but also receives the most visitors. The well preserved Doric Temple of Aphaia is a must see and Aegina grows the best pistachios of all Greece.
Its beaches are nothing to write home about however but good enough for a quick dip. Poros is the next scheduled stop and only 5 minutes from the Peloponnese. Its beaches are quite good and the town fun. For ruins it has a well placed temple but in poor condition. Further south lies Hydra with rocks to swim from vs. beaches.
Its historical atmosphere, car free environment and sophisticated shopping and dining establishments make it a favorite of many well heeled weekend Greek visitors.
A few artists, both foreign and Greek live on Hydra. Spetses, farthest south and actually in the Argo-Saronic Gulf is best of all for its slower pace, sandy and shaded beaches, greenery and good restaurants. It also takes the longest to get to and consequently has fewer tourists.