This is just me...
Unless, as suggested, this trip to an island is for a mileage run, I would NEVER attempt a 1-2 day island jaunt in February. You will hardly see anything and you run a good risk of travel issues. There is so much to do in and around Athens I could spend a week or more there. Walk the Anafiotika neighborhood around the base of the Acropolis. Some same it is more Greek island- like than the Greek islands!