The Ionian Islands of Greece located between Italy and Greece, are not as well known in the USA as the Cyclades and Peloponnese, however they are some of the best. In fact i think one could say that the beaches of Paxos and Anti Paxos are maybe the best in the world.
These islands can be reached by daily ferry from Corfu another amazing Ionian island, in 1 hour for around 20 euro. There are direct flights to Corfu from London ( 3 hours ) in the summer from as little as $100 USD round trip. Or from Athens ( 1 hour) as part of a longer trip to Greece from under $70.
The trick is to stay on Paxos and rent a boat, or take a short ferry ride to the beach on Anti Paxos.
You can rent a house, or stay in a local hotel, the main town on Paxos is very cute and is harbour front, the harbour in the summer is lined with small yachts on charter or private owners, there are many waterfront restaurants serving up fantastic greek food.
A great an inexpensive hotel to stay at which is a short taxi from town and has also its own beach is:
Paxos Beach Hotel