There are lots of good places to eat I am sure you will find for yourselves but I will just mention a few I have tried. After your first 24 hours you will find the things that attract you.
Cocodile, 47, Promenade des Anglais. One block west from Negresco Hotel: Open all day but best for a drink/aperatif, lunch or dinner: turn left out of the apartment walk towards sea, cross road right and a few steps to right. (*Just a few steps past there is also the bus stop where you can get the Express bus to the airport if you have an early flight). charming, friendly, helpful waiters. good food at reasonable prices. excellent house wine not overpriced, but if you are a wine buff, there is also a good cellar by glass or bottle. 0493444296
Forum Jorge Francois. Small offbeat lunch place with 4 star chef. €11 for 3 course menu. To be found in side street basement of the large church almost opposite. 9 rue Cronstadt telephone 0493043460. 3 minutes away!
Sarao turn East along Promenade des Anglais about ten minutes walk, just after the Casino. Good food a bit short on atmosphere except on Saturday night when there is music. watch out for the " menu" with some small print catches!
Lou Ginestre Restaurant set high above Nice, opposite the Ginistiere Hospital has a charming garden and the food is excellent, it does so well in fact that it is only open on weekdays, you can catch the 22 bus in Rue Dante one block away, it takes you to the door of the restaurant, but best to ask for Arrete Hopital l'Archet2 (arret opital archay der) coming back get off at Bottero/Gambetta. Really worth a visit. It is open normal lunchtime and 7.30 pm on in evenings.
On The beach the two best I have found are Blue beach and Sporting both East direction from where we are. Lovely to have a light lunch there and some of them are open in the evening.
There are also plenty of good brasseries with different cuisines in Rue de France
Supermarkets - Carrefour across the road in Gambetta, almost opposite apartment is best and cheapest Opens at 8.30 am, bakery opens at 6.30 am. The very nearest supermarket is turn right, same side of the road in Rue de France. But a little more expensive. If you are heavily into Organic food there is a very large "bio" food shop opposite the apartment block.
The Flower market in old town (known by locals as Saleya) is open every day mornings. Only Monday it is antiques. Really worth a visit but can get busy, many vibrant cafes and restaurants. Cafe des Fleurs offers pleasant lunchtime menu. It also has Wi Fi as does Cocodile!
Don’t buy fruit in the place a couple of shops away from us in Rue de France. It is expensive, and not good, about 30 metres along on same side of the road there is a tiny shop selling Italian fruit etc. that has not been sprayed with insecticide.
For ice cream, sorbets etc. lovely fresh cold drinks, the oldest and best in Nice is about 20 metres away in Gambetta on same side of the road on way to beach. In the same short stretch there are places to eat, plus Russian food shop and others. The cafes and restaurants in this short stretch are fine and good value, but a bit noisy! Avoid the corner icecream place, it is expensive, only thing going for it is a sea view.
For Restaurants open in the evening a bit more pricy than just eating around but an experience..... Rotande at Negresco where also is The Relais bar with jazz and music – is a nice place to chill out with a partner. As it was their centenary 2013 there is now a Salon Versailles Champagne bar open from 12.30 midday - 1 am with live music and DJ. Pop in to the hotel 2 minutes walk away and check what is on offer. However their entertainment changes so worth checking with the concierge.
I will not attempt to tell you all the places to go, enjoy and visit as it would take a whole book, but there are bound to be suggestions online of the kind of things interesting to you. It is such an individual taste better to look up the things you love to do.