The best way to get around the island is by renting a car or a quad bike. A standard car or bike rental costs around €35-€50 per day. Taxis are also available, but they can be expensive, especially during peak season. Public transportation is limited, but there are buses that run between the main towns and beaches.
If you have more time, consider adding a day trip to the neighboring island of Santorini. For a more relaxed trip, consider extending your stay to 3-4 days, so you can fully explore all that Mykonos has to offer.