hi justin
Most of the islands nearest to Athens are not served by their own airport and therefore you would need to fly into Athens and ferry across from Pireaus. I am thinking of islands such as Aegina, Agistri, (very popular with Athenians at weekends and quite close to the port!!)) Evia which is an extremely large island and islands in the Cyclades group but it all depends how long you want to spend on a ferry!! You would also need to book your rooms seperately, I think, as I am not aware of any major tour operators serving these islands. You would have to look to the smaller greek specialist operators.
Kath

Hi there, I asked the same question a while ago, it is further down this page.
PS. there are no flights from the north west to Athens on 22nd or 23rd May if that was when you were looking for
http://www.holidaytruths.co.uk/viewtopic.php?p=932411&highlight=#932411