My favorite Greek taverna in Mykonos (I ate there twice during my short stay) is To Maereio (address: Kalogera, 16). Owned by two local brothers (they are twins who grew up on the island), the food is simple and delicious and so flavorful. It is nestled on one of the characteristic winding streets of Mykonos town (Chora), and has three outdoor tables if you are lucky enough to get one. Alternatively, you can sit inside or even have a meal at the bar.
You absolutely cannot go to Maereio without sampling the zucchini meatballs. I could throw down half a dozen of these now as I write this. So good.
Apologies in advance for the picture quality here, but we also had two main dishes, beef with rice and crispy potatoes, as well as a plate of spicy sausage in a tomato based sauce with peppers. These were delicious "home-cooked"meals that hit the spot after a long day at the beach.
And some extra potatoes with dill yoghurt for good measure:
The brothers will probably offer you an after dinner shot of soumada, a traditional non-alcoholic drink flavored with almond and rosewater. It will be the perfect end to your Mykonian dinner.