I have lived on Mykonos for the last eight years and it was the best move I have ever made. Buying out here has eased up slightly but you still get tied up in buerocracy. Prices vary (like everywhere) depending on which part of the island you want to buy and is dependent on the size and style of house you want. In villages like Ano Mera prices are cheaper than on the coast. I would avoid anywhere in Chora like the plague. I think I have one of the best places on the island, overlooking Psarou bay, near enough to town to get in when you want but far enough away so that you are not in the thick of things in July and August when the population increases from 10,000 (winter) to almost a quarter of a million.
My advice to anyone thinking of buying here is to visit at different times of the year, winter is completely different to summer but then if you are not thinking of living here permanently you wouldn't be bothered by the winters.
Once you reach Full Membership, feel free to send me a message for any more information or advice I can offer.
If you are over here this year come and say hello, I can be found on Psarou Beach each day at Cavo Psarou Restaurant. https://www.facebook.com/pages/Cavo-Psarou-Cafe-Restaurant/155033404564285

Thanks Peter.
That's really helpful.
We have visited at different times of the year and I love the island when it is quiet.
We know Psarou Bay and we'll certainly pop along to the beach when we are over 🙂

Best fo luck and enjoy!!