We dock in Mykonos for 6 hours in July and will be traveling with our 8 year old son. Can anyone offer recommendations on what to do/how to best use our time there. A beach is not a must do since we are going to Puerto Rico in June and will have pools in our ship.
You can spend the time easily just wandering Mykonos town, looking around the harbor, getting lost in the shops back in the winding narrow streets, heading out towards the windmills, stopping for a snack or glass of wine.
If you want more of a destination, in the harbor you can buy tickets to hop one of the boats going out to Delos, a very important ancient Greek site, that likely would take up 3 hours easily.
The beaches are very nice, Puerto Rico probably better, if you do decide to go, you would need to walk up to the bus station above the town, then catch a bus out to the beaches. Taxi would be more efficient of course. Of the beaches, I would recommend Manoulas or Psarous beach, Paradise Beach may be more of an education for your child than you like.
If you're on a cruise ship they probably offer an excursion out to Delos, the world heritage island. That's what I recommend. It's the best family outing you can have on Mykonos without focusing on swimming at the beach.