This was both our favorite and most hated port due to the cable car experience to get back to the water. The city is situated way up on top of the mountain and to get there from the water, you take a cable car up or walk the 500+ steps (or you could take a donkey up the stairs too). Going up is no problem, but coming back down causes a LOT of problems. Get in line to the cable car by about 11am or just forget about it. There is no organization and about 5-600 people in line waiting for the 36 seats in the cable car. There were 3 cruise ships in port the day we were there so expect ridiculousness and rudeness and shoving.
The sites in the village and to Oia were amazing, but definitely ruined by the experience with the cable cars. Just plan ahead otherwise skip it altogether and just spend the night in Mykonos.