It depends on where you want to go. The best months to visit the islands are May, June, early July, September and early October. 

Avoid the dates July 20^th to August 20^th which are the busiest of the tourist season, and late October because the weather gradually becomes rough. If you want to visit the mainland, then March, April, May, June, September and October are suitable months. July and August are very warm and busy. The winter months in Greece are much milder than they are in Northern Europe, but still we get heavy rains, low temperatures, strong winds and snow (in the North). The majority of the tourist related enterprises on the islands - hotels, shops, restaurants - close down, the transportation to/from/between the islands becomes irregular and weather dependant, the sights and museums close earlier and many hotels on the mainland close down for renovation and maintenance. Good destinations are Athens, bigger islands with many permanent inhabitants like Crete and Rhodes, and certain mainland areas in Greece that offer Winter activities (e.g. ski centres) or can be easily visited throughout the year like Delphi, Nafplion, Meteora, Karpenissi, Mani etc….