Would highly recommend Isidoros' villa for anyone coming to mykonos but not wanting to stay near the big party beaches. The view is spectacular and with a large outdoor entertaining area we rarely felt the need to leave the villa at all. If not hiring a car (we didn't see the need for 3 days) then I would recommend organising transfers through Isidoros - we tried to get the bus from mykonos Town but it is irregular (Isidoros's wife met us in elia and took us to the flat), he was also able to put us in touch with one of the neighbours who drove us to the large supermarket and back for 20€. Would recommend this as elia Beach does not really have grocery options. The villa is a short but very steep walk up from the beach - worth it for the views you get at the top though.
If looking to go into mykonos Town for the night we were able to get one of the shuttle buses from a nearby resort for free and then a taxi back was 35€.
Would definitely come back.