Without stating the bleeding obvs. any of the Greek islands that don't have an airport are going to be much quieter than those that do. I lived on Corfu for just over a year, which is about as touristy as it gets. Our favourite islands for escape were Serifos and Folegandros.
ETA: Folegandros is a ~7hr boat ride from Piraeus. Most people, having flown in to Athens, aren't going to embrace the prospect of 14 hrs on a boat cutting in to their holiday time - so they don't go there. Greeks holiday there. Prices for everything are accordingly low.
Without stating the bleeding obvs. any of the Greek islands that don't have an airport are going to be much quieter than those that do. I lived on Corfu for just over a year, which is about as touristy as it gets. Our favourite islands for escape were Serifos and Folegandros.
ETA: Folegandros is a ~7hr boat ride from Piraeus. Most people, having flown in to Athens, aren't going to embrace the prospect of 14 hrs on a boat cutting in to their holiday time - so they don't go there. Greeks holiday there. Prices for everything are accordingly low.