Here are a few suggestions;
Bicycles can be rented at many locations in the streets
Boat trips from Nice Port to StTropez
Visit to the Chagall Museum
Cannes Film festival by train
Ventimiglia market in Italy
The Nice Jazz Festival
The aquarium of Monaco
The Old Town with its many restaurants
The antiques market on Cours Saleya
The Monaco Grand prix
Promenade des Anglais beaches and beach restaurants
Your hosts will be happy to suggest places to visit depending on the season.