In October, Athens has an average maximum daytime temperature of 24C, falling to an average of 15C overnight. There are typically 8 wet days in the month: http://www.bbc.co.uk/weather/world/city_guides /city.shtml?tt=TT003830
(Use the links, under 'Average Conditions' for the figures for Naxos, Thessaloniki & Trikkala).
Have you looked at the temperatures for Cyprus or Crete? Some ot the Greek Islands are getting towards the end of their season and may be running down if not very busy.
It depends where in Greece you are thinking of. The Ionian islands are getting very unpredictable in October, They are greener and therefore get more rain but you can be lucky even in Ocotber. The islands on the other side of Greece towards Turkey are much more barren therefore less rain. October should be ok if you choose these islands.