You will be hard pressed to do the islands in a week. I would think about going down the peloponnese, sailing from port to port. There are several charter companys that work out of Piraeus near Athens, we used Nelson and were very happy.
there is a website that is very comprehensive and talks about many destinations around the world. www.sailing-advisor.com
They also have listings of charter companies at the end of each destination page.
One week will allow you to sail confortably along about 100 nm. I assume you have limited time, hence you should sail out of the Athens area and visit the Saronic gulf, tentatively go as far as Hydra/Spetses/Porto Heli, no way beyond that. You might also encounter rainy and cool weather, but still you will be able to swim and enjoy the sun during most of your trip. I wish you find a helpful skipper. Consult also the following website: http://www.sailingissues.com/