Head to one of the famous Greek islands. Not a random island though, but THE MOST famous Greek island, "the island of the winds", Mykonos. You will take the morning ferry to Mykonos. After check-in, one way to get into the atmosphere of the island is to spend your afternoon by the sea at a beach bar or restaurant on the beach of Ornos.
In Mykonos everyone celebrates summer and the party starts in the early afternoon. Alternatively, you can wander around Mykonos Town with its whitewashed houses, variety of boutiques and amazing restaurants.