3 days is just about enough for Athens, at least if you're planning to see more than the Acropolis. Look to head to the *burbs* of Athens...out by Glyfada and/or Vouliagmeni for a nice beach/swim. When I can entice family and friends to join me on my trips to Greece, I lean towards these combos based on past experiences:
Lesbos/Chios
Chios/Samos
Samos/Patmos
Kos/Kalymnos
Naxos/Paros
Naxos/Amorgos
Syros/Tinos
All offer a great selection of nice beaches, traditional culture (much of which, sadly, seems to be disappearing), photogenic towns and great restaurants.
Mykonos and Santorini are the two most touristic islands in Greece, and thus also the most expensive.
Santorini is a must see island due to the fantastic scenery and views.
Both islands are swarmed by cruise liners daily.
Thessaloniki is probably the most beautiful city in Greece. It has a lot of Byzantine monuments spread throughout the city. Thessaloniki is famous for its delicious cuisine, considered the best in Greece. So if you like Greek food, in Thessaloniki you'll eat the best of the best. You can visit Archeological and Byzantine museums, folklore museum, White Tower, Castle area on the hill, Hagia Sofia temple, Saint Demetrius Temple, go for a small cruise (1h) to Perea to relax next to the seaside and have nice sea food, also swim there. If you really want to see all of the beautiful parts of Thessaloniki (and there are many), definitely rent a car in Greece.
You can go by bus or train to Edessa town (1-1.5h), where there are waterfalls.
There are buses to Halkidiki, it is just outside the city, so you need to go there by taxi or bus. It might be easier to go by car to Halkidiki, since the buses go to main towns or villages and might need to go to the hotel or resort by taxi from the bus stop.
I would suggest to go to the second peninsula of Halkidiki, called Sithonia. Favourite place is Vourvourou, and some more like Kavourotrypes and Sarti, also visit the other side of peninsula, like Toroni and Neos Marmaras.