If you visit Mykonos in winter, just remember that most shop at Little Venice will be closed. Boat ride to Delos Archaeological site might be limited. You might not be able to take the boat to swim at the hot spring. It all depends on what you want to do in Mykonos. Visit in low seasons or shoulder season means that there are less tourist. You might not be able to do some of the activities that I mentioned above. However you still could enjoy most of the major sites provided that the days you are there are not during Easter holidays. There will be less crowded with tourists. Driving around will be easier as well as parking will be ample except kn the Mykonos Harbour area where it is usually very pack as most restaurants are located around there. Greek are faithful Orthodox Christians, any Christian festivals all the shops will be closed. Just have to be mindful of this. Hopefully this helps you as you plan for your trip.

Hi Elaine. Our cruise ship docked at the new port and there were buses that went to the old port and from there it is a short walk into the town. If you just want to walk around the shops and cafes you don't need to book a short excursion but if you are being offered more than that it might be worth considering. I spent a few hours wandering around the streets before eating at a taverna in a back lane away from the more touristy spots.