I fear that the books I have identified so far for some countries are not always terribly highbrow, but I don't think anyone can really have grounds for complaint here. Although it does wander round the eastern Mediterranean a bit, with excursions into completely imaginary geography, most of the places described - and, crucially, the start and finish of the book - are set firmly on territory which is today part of the Hellenic Republic. It's the book most often tagged "Greece" on LibraryThing and Goodreads, and it's far ahead of any other books set in Greece in terms of ownership. (With a small caveat explained below.) It is, of course:
The Odyssey / Ὀδύσσεια, by Homer
Once I rule out certain books for being insufficiently set in Greece (or not at all - those being Middlesex by Jeffrey Eugenides and The Republic by Plato), the clear second place goes to a play of the classical era - with the wrinkle that on its own it does much better on Goodreads, but bound with two other plays by the same author with a closely related historical setting it does much better on LibraryThing. It is:
Oedipus Rex / Οἰδίπους Τύραννος, by Sophocles
The top modern book set in Greece is a 1994 work by a British novelist with a French name, which was adapted for film in 2003. It is of course:
Captain Corelli's Mandolin / Corelli's Mandolin, by Louis de Bernières.
I think that's all very satisfying.