Mykonos hotels with FREE parking are as scarce as virgins on this island. Still there are a few. This is what they report on booking.com and often on their sites. It helps to double check with them prior to booking, if it is a deal breaker for you.
Mykonos Hotels with FREE Parking
In case you stay at a hotel or rooms without parking facilities, then consider these parking spaces in and around town. You can find them here