Zakynthos, Turtle island in front of Agios Sostis. The famous ship wreck that you see on so many Greece postcards and advertising is on Zakynthos, you can see it when doing a boat trip around the island with a bbq. Oh, and try the ouzo.
Corfu, westside of Greece, very up north, very green island, north is great to see by jeep safari, you can explore the south with a rental car. Rent a motor boat. Go parasailing or in tubes behind a motor boat.
Rhodes, you can even do a day trip to Turkey, bring your passport.
Eat and drink: dolmades (rice in wine leaves), ouzo (very strong! Drink with 7-up if you don’t want to go for the pure stuff), mazethes, a mix of different Greek food