If your first time in Mykonos (we have been many times), also depending on the weather, (eg. August can be killer hot and your only desire will be going to the beach), I would take the water taxi which is adjacent to the ship dock - hmm I think there are two piers now. (Cost about $3.00 euros each way per person or the walk if weather is pleasant is about half an hour). Arrive, get a lay of the land, enjoy the Greek version of little Venice, (absolutely adorable, get lost in all the little narrow alleys, just enjoy the town. Walk out to the lighthouses and, if time permits, you can take a cheap shuttle (small vans charging around 10 to 15 euros a ride are at the edge of Mykonos town willing to ferry you to the various resort beaches and spend some time there on the beach. Watch the time.