There is a nationwide sale to Athens, which will allow you to visit Santorini or Mykonos for 1/3 of the usual price! All you need to do is book the right flight to Athens, and then use Google Flights to search for roundtrip tickets from Athens to Santorini or Mykonos. These roundtrip flights could be found for as low as $30 on budget airlines like Ryanair. Just remember that budget airlines charge extra for everything (luggage, carry-on, choosing your seat).
Airport Code: ATH
Airline: Multiple Airline – AA, BA, IB
Availability: January – May 2017
Nearby Airports? Yes, a few available dates from OAK for $10-20 more.
Outbound: 2 – ORD, MAD
Inbound: 1 – LHR
Search Here (Google Flights)
Sample pricing (aa.com)