We've been to two islands early in the year once, not sure if it was February or March. You really have to be tolerant of all kinds of weather at that time of year: We had sun to the point of getting a sunburn, rain, thunderstorms, snow.
Unless you focus only on the "big" destinations like Athens or Crete, you will have to do most of the organizing by yourself. I don't think you will find many package tours at that time of year except for those big places. In the summer destinations, most of the restaurants will be closed.
And be prepared that Greek hotel rooms are not meant for cold weather. The only "heating" device might be the AC, and in our case, that did not get the room above 15°C.
Now having listed all the downsides, here are the advantages – and we loved it:
We had the islands to ourselves. No tourists; only us and the locals.
We had the greatest choice of rooms because the locals were just happy about a bit of off-season income. We ended up with a huge apartment for very little money.
The flower season was beginning, and hiking was lovely (except on the days with pouring rains).
As a history buff, Athens of course is going to be on your list. If you plan to go anywhere else, I'd put Athens at the end of the tour… for safety reasons. With the weather being a bit unpredictable, you might get stranded somewhere (like on that trip of ours, after half an inch of snowfall, all island flights were cancelled), so you may want some buffer time to be sure you catch your return flight.