2 things you plan donīt make sense: 1st staying at Cap Ferrat and Nice, 2nd staying without a rental car if you wonna see something around.
As others mentioned Nice and Cap Ferrat are near bye. If you wonna do St. Tropez and Cannes + another hotel stay there. Itīs quite a distance from Nice. If you wonna see Negresco go there for Lunch or Dinner at their 2 star restaurant. There is a lot to see in the region so you can spend 7 nights at Cap Ferrat without problems. It is possible to reach some restaurants from Cap Ferrat by Walking but much more interesting options are available by car. Restaurants at FS are totally overpriced.