Sleep in Nice. Move by TER. Add a car only on the day you leave the rail line.
3 days: Nice and the rail towns
Day one Promenade and old Nice. Day two Matisse or Chagall plus a beach hour. Day three Antibes or Monaco by train.
5 days: coast plus inland
Keep the three-day core, then Grasse one day and either Cannes or an Esterel cove day. That is enough without hotel-hopping.
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