Ronnie at the Irish bar near the culture centre cooks a British style meal if you want something like pie and chips.There is a Burger King opposite the Carrefour and there are places in the central old town which serve Turkish meals. You have quite a choice really.The supermarkets also have cafe's. Opposite the bus station is the Gar Lokanta which is open all hours.
If you want a more expensive restaurant there is the Sarafane at the Atapark Hotel along near Karagozler 2 or Kale Park in Fethiye towards the ruined castle.
Ovacik and Hisaronu still have restaurants open during the winter too,though not as many as in the summer season.