We too walked past this restaurant a number of times 2 weeks ago
The Chill out Restaurant and Cocktail bar on the babadag mountain road . Should there be any dispute the address is Oludeniz Beldesi,Ovacik Mahallesi, Babadagi Yolu Uzeri-Fethiye. It did seem busy although the seating is the full length of the front of the restaurant and elevated, which makes a difference. When we used it on our last morning for Breakfast the food was very nice and staff were pleasant. The thing we were certainly not impressed with, was the soiled tablecloths and a waiter wearing a dirty t-shirt.