From Mykonos town take the bus from the main road on the south end of town (The fare is cheap less than 50 cents) to Plati Yialos Beach. If you stay at Plati Yialos, you will be given a chair and umbrella at no charge if you have lunch at one of the hotels.
From Plati Yialos Beach small boats take visitors to Paradise and Super Paradise and you can rent boats at the dock to go elsewhere. The fee for the boat taxi was about $3 for all day. There are tavernas and public restrooms at all of these beaches. Full Nudity is allowed at Paradise and Super Paradise. You will notice this is at the far end of the beach in both cases. Topless is not uncommon at Plati Yialos. Other beautiful beaches are Ornos Bay, Psarou, Kapari, Aghia Anna, Megali Ammos, and Aghios Ioannis. If you are not sure what beach is for you, stop at the Mykonos Accommodation Center in the center of town and ask the friendly staff for help.