Mykonos is well known as the party-island, but in reality Mykonos is the place where you can do whatever you like.
For example, you simply want to sit alone and relax.
In that case, you could visit the Ftelia Beach, located on the northern part of the island.
You are maybe wondering what does Ftelia (Φτελιά) means? Ftelia means "elm". In case you have no idea what the elm is, well it is a tree. And just for curiosity, Elia means "olive".
Ftelia also has the historical significance, as it was settled in the Neolithic period. If you are very curious, you could learn more by reading this scientific paper. It is not boring, I'm promising:
https://s3.amazonaws.com/academia.edu.documents/6981735/2008Horizon_NPC.pdf?AWSAccessKeyId=AKIAIWOWYYGZ2Y53UL3A&Expires=1510682348&Signature=pzsnESVw7HL6YxsWrjPKiEO0Y7w%3D&response-content-disposition=inline%3B%20filename%3DEconomy_and_occupation_in_the_Cyclades_d.pdf
Of course, you would like to see the picture, so, here it is: