There are numerous islands to see, but with your time frame I would suggest one of the closer ones to Piraeus such as Aegina or Hydra, two very popular day-trip islands, both offer something different. Hydra has one of the most beautiful waterfronts in all of Greece and there are no motorized vehicles allowed on the island, everything is transported by donkeys which gives you a feel of the "old" Greece. Aegina has more to offer as far as activities and things to do with one of the best temples anywhere in Greece, an abandoned village in the hills, beaches, hiking and a nice main town of Aegina and is known as the Pistachio Capitol of Greece.. Hydra is more for just hanging out, eating, having a drink, people watching but there is some good hiking, too. The village goes uphill from the waterfront with very lovely homes and is much quieter than the waterfront. Both are a short ferry ride from Athens.