You can be lucky with the weather in March - or very unlucky! We sat outside
in the sunshine at a harbourside cafe on Syros (Cyclades) on Christmas
morning 2 years ago - and this year our friends phoned us Christmas day to
tell us it was freezing cold and snowing! We spent a wonderful Easter with
our friends one April when it was warm and sunny every day, spending time in
Athens and then back to Syros (not a 'holiday' island). Athens was busy but
not frantic and there were no queues for the Parthenon!
I would advise heading for the larger islands if you go anywhere and staying
in the main towns where they are more geared up for year round visitors.
Perhaps Crete or Rhodes which should be warmer anyway.
Forget wanting any kind of beach activity but it would be a good time to
visit all the ancient sites without stifling heat and the unbearable
hoardes of the summer months