On our August 22 Odyssey trip, in Mykonos we docked, the water taxi was at the end of the peir and I think was a few euro each way. There were taxis and then the coaches for booked shore excursions.
It’s possible, of course that you could be tendering depending on the other booked arrivals as a random date in June suggests there’s 5 other ships in alongside Odyssey
https://cruisedig.com/ports/mykonos-greece/arrivals