We always spend Christmas and New Year in Greece.
Some islands are still lively. Syros, the capital of the Cyclades, for example. It is also possible to fly there in around an hour and internal flights are relatively cheap.
Having said that I would stick to the mainland. There are ferries but they are less frequent and weather, especially high winds, can make them unreliable.
Nafplio is an excellent option. It's easy to reach by public transport, if you don't want to drive, is a beautiful little town and is always lively at that time of year. We were last there for Christmas 2011 and wrote up our take then.
We're going to be in Athens at that time this year, so let's both keep our fingers crossed for good weather!