Hi Simone. From Izmir you will not find any gulet cruises. I would suggest you to start anywhere close to Dalaman region (Gocek, Fethiye, Marmaris) or Bodrum region. Most charters depart from there. Antalya is also an option, but gulets there are not something you might be interested in (more or less)...
Because of better nature and nicer sea Dalaman region is for me nicer....If you did not yet book your flights, you can also consider Croatia - it is a bit nicer :-)
When it comes to companies....I would recommend ours....but then this would be direct advertisement so I can not :-)
Mitja about 4 years ago