Source: https://en.wikipedia.org/wiki/List_of_islands_of_Greece
And it would not even have to be uninhabited I guess. Greece is very poor and really needs any investments it can get (as is in the article).
Given the size of Greece (incl the islands) everything is nearby. With a budget of billions it would not be a problem to spend (only once) some money for a new airport (I guess now its spend every four years in some city to modernize their nearest airport).
I do expect, however, that most of the uninhabitated Greek islands are too small to be useful for this. You would need 10-20 different stadiums, 2 km straight water to hold rowing events, and wouldn't want to have marathon runners, competitors in the 50 km walk, or those taking part in the cycling road race to do 1 km rounds. Let's say 100 square kilometers to host all the courses (except for sailing; there's plenty of sea for that), bare minimum.
Also, it would be a challenge to feed the competitors and the spectators on an island that size. Greece isn't known for its green islands, and looking at that list, I notice that, for example, Tinos and Paros, at around 200 square kilometers, have a population of less than 10,000.
I would think you would need something like Kos to host the Olympics, and even that would be an enormous challenge. The 'normal' population of around 33,000 would increase by 20,000+ competitors, officials and a zillion journalists, and you likely would have to ferry or fly in half a million spectators every day, and all of them would need food and drink, and working 3G.
Frankly, it is probably better to create a new island than trying to find an unused one.
Look at the BER disaster, it was supposed to open 2007 and most likely won't open until way after 2017.
I believe building a permanent Olympic site in Greece would bring similar delays...
[0] https://en.wikipedia.org/wiki/Berlin_Brandenburg_Airport [1] https://en.wikipedia.org/wiki/Elbe_Philharmonic_Hall