Hi Fredgoblu,

Timing is good in both cases. End of May will be cheaper and less crowdy. Mid July is going to be very hot but maybe you will find the water in the sea much warmer than beginning of June. So it all depends on what you are after.
If you do Athens in 3 days stay somewhere central - Hilton has a sale on at the moment and visit the ancient monuments and the museums and dont forget to go up in Lycabetus hill for the sunset. Just outside Athens you will find some very nice beaches as well. If you have enough time I would recommend going all the way to the Sounio temple (there is a bus that can get you there). Also just 30 minutes away from the city center you can get the tram to a few Athens beaches (not all that great as the ones 1-2 hours drive away) but with very nice and relaxed beach bars.
Santorini has great views and the typical aegean architecture. Its a very picturesque place with the best village being Oia. Take a daily boatrip to the smaller islands of the volcano and dive into the thermal spots right into the volcano. The beaches in Santorini though are not all that great just because of the dark sand, stones from the volcano so you might want to choose an island with beautiful beaches for the rest 3 days. Mykonos has some very nice beaches and great nightlife but you may find a bit too noisy (end of May should be okey though). Syros is a very nice island with nice beaches and great tavernas (also cheaper than Santorini) or you could try Paros. Seeing that these islands are basically on your way from Athens to Santorini are easy to do.
If you want though to visit a different type of island get outside cyclades and visit Hydra, Poros or Spetses from Athens with speedferry. The other island groups in Greece are very beautiful as well but you will not have enough time to fit them in.
Hope you have a great time.

Elina