I would seriously consider flying to Athens and then taking the Blue Star Ferry if flights from Athens to Mykonos are a problem. We took the Ferry and it was an enjoyable trip seeing the coastline. The ferry is more like a cruise ship but make sure you upgrade to the Air Seats, which isn't much more but well worth it. Here are some pictures of the ferry etc.
https://plus.google.com/photos/11172...67652374501729