You should note that in France, dinner is usually served after 7p.   In the summer, or when going to a restaurant, it can often be later - a 8p or 9p reservation is typical.

Traditional Nicois French 

You can try 'socca' which is a crepe like shape made of chick pea flour.  Sounds wierd, but it can be quite good.  You usually eat it as a snack, with a bit of pepper on it.

For meals, typical nicois dishes include 'Farcis Nicois' (stuffed vegetables) or Daube & Ravioli (a stew with small raviolis). 

The best area for such meals is in the old town of Nice, around the flower market.

Seafood

Very big here, not unexpectedly but you need to be prepared to pay. Cafe du Turin in Place Garribaldi is the most well known. Also Boccacio in the Zone Pietone

You an also travel down to St. Laurent du Var (near the large Cap 3000 mall.)  There are many seafood and other restaurants along the port, which can be nice for a stroll.   While some can be quite pricey (and not always top quality seafood), one that is not promoted as a seafood restaurant but which has reasonably priced excellent seafood is Le Petit Flor.    Right next door is a piano bar if you want to extend your evening.

Michelin-starred top tables

Best, by far, is in Biot, in between the glass shops and the village is Les Terrailliers.   The surroundings are lovely and the food is classic star quality.    The service is excellent, and not snobbish as is the case is many starred restaurants.