In my opinion it would make no sense at all to rent a car in Athens and take it to various islands. This would certainly complicate your travel and reduce ferry options. I suggest you consider renting on each island- --not a problem to do.

Each Greek island belongs to a chain of islands and generally speaking it is least complicated to do your travel within a chain of islands as this gives the most straightforward options with respect to ferry travel. There are "local" ferries that run between chains or between specific islands but it depends where you are and time of year etc.

Travel between chains can involve going back to the main port near Athens and changing to a ferry line that services that group of islands. We did a trip several years back involving four islands and not all were in the same chain so could give you more specific advice if you wished to e-mail me privately.

Art Sauder Vancouver