Joan,
That's a very ambitious plan for a visit of only four days, and not really practical IMO (even if it is "doable"). Keep in mind that you have to allow time for travel between airports, waiting times, check-in, security and the other usual hassles. If there's a "problem" with any leg of a plan like this, it will affect the rest of the plan.
Were you planning to travel with carry-on only? The European airlines have some VERY restrictive baggage limits, and many allow only ONE carry on item per passenger. That doesn't mean "one plus a personal item" it literally means ONE ONLY! If you have heavy checked luggage, you may face overweight luggage charges.
The other thing to remember is that many of Greek Islands are somewhat "quiet" during the winter and the weather may not even be too favourable.
For such a short trip, you might want to stick with Athens and a few stops on the Peloponnese peninsula (Hydra might be one possibility?).
Good luck!