In Turkey, if you would prefer going to a beach resort in April, be aware that the water temperatures won't be warm like the summer but it's definitely worth visiting and more than %50 of hotels are open at that time of the year and they won't be crowded as you're traveling in offseason of Turkey.

But for cultural visits within the Aegean and Mediterranean area, the weather would be perfect. However, from Athens, the only Turkish holiday destination that is served is Izmir.

Never been to Santorini but I assume that it would warm for a beach holiday but Crete would be better if your main purpose is a beach holiday.

Also, double check the hotel(s) that you would stay as they could be a tourist scam ( anywhere in the Mediterranean ).

And as KLouis mentioned, you could fly even to Northern Europe or Ibiza with a 3-hour flight from Athens.