Take your pick of one of the restaurants in town, or one of the pubs. Bookings are a good idea at the restaurants during the season.
There is a caravan out the back of the Potshot Hotel, which serves burgers and chips in the open air. There are a couple of take-away places and cafes.
Expect to pay a premium for eating out in Exmouth. Wages are high, and food costs expensive. A Chicken Parma which may cost you $15 in Perth may cost you $35 or more here.