Beach day in Nice

I'd say Castel Plage, at the very end of the beach right by the Chateau elevator: it has the best views.
No idea about the food.
You are aware it is a pebbly beach, right? You don't 100% need beach shoes but they are nice to have. Also, if there are kids, beware: the beach is steeply sloped, you cannot really wade.

If you are willing to travel a bit, have a look at Plage de la Mala near Monaco (at Cap d'Ail train stop).

The beaches in Nice are rocky not sandy. We have stopped at a few for drinks at sunset, but I can't imagine spending a day at the beach like one might do in Hawaii or the Caribbean.

We stayed at Beau Rivage which offers what you are describing. It was open to non- hotel guests when we were there. You won’t want to spend a whole day there.

The beach clubs tend to differentiate themselves a bit on vibe and food. Price can vary a bit as well. Castel has the best view down the beach but the biggest rocks and a pretty steep entry. As you get down well past the Negresco, the pebbles get smaller (still not tiny) by the time you get to La Vela/Voilier plage. You won't notice them in the club due to walkways (and even sand) but once you head to the water, yes. Here's a good reference: link (I know the site looks dated but the info seems relatively current)

You can also take a short trip out of town. Juan les Pins and Cannes are easy to get to by train and the beach is not far from the station. The same with VilleFranche-sur-mer, but the beach is best described as large grain sand. Mala is beautiful in terms of surroundings but peak season pricing at the private clubs can be quite high.