Mykonos in February?

Yes, if you want to see Mykonos without hordes of tourists, with most shops, bars, restaurants and cafes closed and beaches all but deserted. If you're after complete peace and quiet and don't mind cold, wet weather it's worth it.

I agree with Lee. I'm often in Greece in February or March and most of the islands are dead. February is also the worst month for weather.

If for some reason February is the only month you can make it there are a couple of options worth considering:

Nafplio on the mainland is a beautiful little town and lively all the year round. It's also relatively sheltered, certainly as compared to the islands, and you can get some reasonable days.

If you really want to be on an island Syros is the capital of the Cyclades and busy all year round. Ano Syros fits the bill as a 'white cubes straggling up hillside' Cycladic town and Ermopolis, the lower port, has some good eating places and a nice town square.

Alan

...and if interested in hitting an island, consider flying. Ferries will be fewer, weather rougher, schedules more prone to cancellation.

There is a reason that the islands function primarily in the summer. Jan and Feb are tough months.