gtanaki, the answer about charter boats & planes is the same as the famous one about a yacht, if you have to ask what it costs, you can't afford it. You're going to have to see if you can get out of your Santorini rental. and besides --- do you have ANY idea how long it takes for even a fast boat to get from the Turkey Coast to the Southernmost part of the Cyclades??? Time after time, season after season, we implore newcomers NOT to book accommodations until they've researched the logistics ...
If you would look at a map, you'd see that SAMOS is only a 1-hour ferry ride from Kusadasi, and has some wonderful beaches on which to relax. For more luxury, look at PATMOS, which is the secret getaway for Greek celebrities and VIPs ...a google of Patmos Villas will show you a big array of lovely places & beaches. Ther may not be a direct ferry from Kusadasi, but a quick ferry to Vathy on Samos, & you can ferry to Patmos in 90 minutes or so.