I’m currently in Aix En Provence having just come from the Riviera. Assuming you are going before the end of September, as others have said, given the amount of time probably best to just bounce around between Antibes and Menton. A great train connects each of the beach towns. You would need a rent car to really explore deeper than the immediate surrounding areas, but I’ll say that parking in the actual beach town areas really sucks. A few thoughts:
From the Eze Sur Mer train station, you can hike up the Nietzche path to the old preserved village of Eze. It’s touristy to be sure, but still pretty cool and the views of the Riviera from the very top of the garden are great. The hike requires shoes and water and you to be in decent shape; it’s not a leisurely stroll but tourists do it every day.
Menton is much lower key with an Italian vibe. Cool town.
St Jean Cap Ferrat is beautiful and has the Rothschild grounds. The Four Seasons on the tip the peninsula is stunning, but hits the wallet fucking hard. Villa French Sur Mer is right there and also cool.
Le Sentier du Littoral is a nice little walk along the coast of Antibes. Need a car for access.
A bit further inland, but St Paul de Vence is a cool preserved village to walk around.
Cannes is a dump.