If you want to get away from the tourists and spend time in a wonderful village without tourists, try May and September for the best months....and early in the day or late afternoon, early evening as the best times

A few wonderful places that are great and deserted except for the locals in May and September and late in the day...but always "authentic":

Near Athens, Sounio at sunset and staying right there near the temple at an older hotel on the beach off season is great, and you are one of the only people at the beach restaurant....just a few locals and you, after you've seen that great sunset through the temple of Poseidon!!

On the Peloponese...Monemvasia is deserted after 4 PM and amazing to stay in overnight.

In the northern half of the country...in the Pilio, Makrinitsa is deserted after 4 PM and amazing to stay in overnight, especially in May when it's mostly deserted during the day.  On the opposite side of the Pagasitic Gulf to the Pelion is Amaliapolis, a very picturesque village.  It has hardly any foreign tourists especially outside July and August.  As it's only a few kilometers from the E75 (main Athens/Thessaloniki motorway) it makes a good base if you want to visit Meteora or Delphi also.

Right outside Meteora's beautiful sights is the village of Kastraki and you can stay in a vineyard very close to the first rocks.

Nafpaktos is also deserted in off season...and near where you cross from the northern half to the southern half of the country.

There still are so many more places on the mainland of Greece that have not been ruined by tourism, where the residents are so friendly and helpful and glad to see you...especially in off season and most especially if you stay overnight.