Possible Clues:

• Cyclades island
• Informal footwear on one backward holiday island
• In Greek island, alliance's taking new heart
• 'Ariadne auf ___' (Richard Strauss opera)
• After border exchange, old German immigrant comes to this island
• Greek island near Paros
• Greek island
• Island where Dionysus discovered Ariadne
• The largest of the Cyclades in the southern Aegean