rome greece or greece rome

I would suggest checking out airfares and then deciding from there.

Sylvia is right. When you have an option, let the fares determine which city you fly into.

Athens air terminal is much easier to navigate if that will help you decide on arriving there or departing from there.

I will add that it also depends on the activities of your itinerary. If both destinations will be spent with general touring, museums, and towns, then it may not matter. But if on destination is more relaxation than touring (Say a Tuscan Agritourismo or Greek Beaches) then I would arrange to do that towards the end of the trip as a nice wind-down.

We're flying into Athens this June, doing the islands, and then will work our way north into Italy. Weather will be nicer that way for us.

Regards.