A block a way from the beginning of Cours Saleya is the Place du Palais, with Palais being the Justice Palace, located here. The street bordering the north side of the square is the Rue de la Préfecture, where you can find several restaurants.
One I particularly like is the Byblos, serving Mediterranean fare from mainly the eastern part of the sea. A little Greek, a little Lebanese and some other dishes from the countries between Nice and Byblos the city, located in Lebanon.
Try a mixed kebab and some Lebanese wine. Who says you have to eat French, when in France? Lebanese meals are about sharing -- order some hummus, yogurt, taboule and pita bread with your meal and share around the table. The owners and staff are incredibly friendly and speak good English. This place might not be the cheapest but it’s certainly not overly expensive. It is definitely worth a try!