Any suggestion how to start and end this Turkey and Greece 10 days trip "
Hi, Yes, cheap airfares into Istanbul. Istanbul is a fabulous city. Three days. Getting to Athens or the islands takes either a flight or an over night bus. Have you considered all ten days in Istanbul with a three day trip to Cappadocio or Ephesus? Getting to Greece even by air and back will shoot two days of your trip.
Your question is a little to general. Can you provide more details on where you'd like to go, when you'd like to go, and what you'd like to see. I start by doing some reading in the library travel section or buying a Rick Steves travel guidebook.