Elia beach is a long sandy beach and exactly next to Agrari beach.
I totally suggest if you are to Agrari beach to go to Elia beach by walking the rocks between as its quite faster than to take your car or motorbike because you will need to make quite a big circle to get there.
Elia used to be a nudist beach but now is quite well organized with water sports, beach bars and restaurants/taverns. You can of course find nudist by going to the small beaches that you can find between Agrari and Elia .
The distance is around 10 kilometers and you need at 15 to 20 mins with a vehicle to get to the beach from Mykonos Town .