There are some great restaurants on the Promenade des Anglais and part of the attraction is looking at the menus outside, strolling along, choosing a restaurant and people-watching. The restaurants and cafes all vary a lot in price and atmosphere and food so I can't give you an exact idea. There's a great seafood restaurant, more than one with speciality French cuisine (eg steak tartare) and some great takeaways selling salade nicoise in French bread, hot dogs etc.
Dinner in Nice happens quite late. There are also some fairly good restaurants up by the market square but they are better for a fixed lunch because the area calms down quite a lot once the market closes. I haven't been to any restaurants in the Old Town but they look fantastic. Sorry I can't help any more but I think the Promenade is the best bet. Hope you enjoy it.