As an alternative to bouillabaisse joints or the hustle and bustle of Le Vieux Port, I'd like to suggest Chez Vincent (25, rue Glandeves, a small alley running parallel to le Vieux Port), which bills itself as a pizzeria-restaurant. We chose not to have pizza (perhaps we should have tried the pizza: when I walked into the restaurant, I saw the pizza maker hard at work at his wood-burning oven, see photo below), but, instead, enjoyed grilled fish and salads.
The grilled fish of the day were rougets. They were simply brushed with oil and sprinkled with herbs and grilled to perfection (see photo). Salads were fresh and generous. The prices were very reasonable (the rougets were 12 Euros). Air-conditioned dining room, plus a few tables outside.
Cheerful service. Closed Mondays and for the first two weeks in August.