Mid-March can be a wonderful time in Nice : you can go skiing in the morning (Valberg, Isola 2000, Auron) and ride a Hobie Cat in the afternoon at Antibes.
I recommend you : hiking in Mercantour regional park, rafting in Gorges de la Roya, drinking at sunset at Hotel de la Chevre d'Or in Eze or at La Reserve in Nice, visiting the perfumeries in Grasse, going to Abbaye de Lerins on the islands in the Bay of Cannes, going to Cassis, the Calanques and Aix-en-Provence...
You will definitely need a car.