We have found that a ceilng fan, blowing DOWN over the eating area, usually stops flies from resting on the surrounding area. A fan blowing horizontally is no good. It must be a good quality fan, set to blow quite hard.
Obviously, the flies will go to other parts of the area where the fan is not blowing, but it will keep the eating area free of them.
As other have posted, a purpose built screen mesh is the best solution.