Just got back from Mykonos - first trip there. There are hotels around the island, but if your parents are young at heart, and like to go out, I would strongly suggest staying at a hotel right in the main town. Otherwise they'll be too isolated. In the peak of summer, it might be too noisy/crowded there, but now it is getting quieter, and the main city is great to stroll around, find restaurants, shop, nightlife (wonderful piano bar on the 'sunset' side of the main town). I would no suggest a hotel, however nice, that is not in the main town. My 2 cents!