Most of the locations in the itinerary are within walking distance, as Chora is a relatively small town. To get to the beaches and Delos Island, you can take a bus from the old port or rent a car/motorbike. Taxis are also available but can be expensive. Expect to spend €40-50/day for car rentals and €10-15 for a round trip to Delos Island.
If you have more time, consider checking out some of the lesser-known beaches on the island such as Lia Beach or Ornos Beach. For those interested in Mykonos' nightlife, head to the beach clubs at Paradise and Super Paradise Beaches.
If you have less time, choose between visiting Delos Island or spending a day at the beaches. Additionally, reduce the amount of time spent at the museums if history and culture are not your cup of tea.