Mykonos, Paros, and Crete, etc.
And there are definitely malls in Athens but in all of those islands I am sure that there are many little stores to shop from. Very pretty!
Athens is a city with shopping malls, amazing tourist attractions and bus services. However, the best beaches you can mostly find in the islands...or at least 1 and a half hour drive from Athens. Also, bus services can be a little slow, very disturbing during the summer when it's 40 degrees Celsius outside, in the rush hour....try combining a few days in Athens and more days in the islands, there are so many of them and they're all beautiful,I personally prefer the Cyclades...
You are looking for a needle in a haystack when you ask for one place, when the whole of Greece, islands and mainland is full of such places. Choose a main area and then ask here again for a specific resort that will be best for you.
Shopping malls? In Greece? Ha!
Greece is a ruin xD
