We went the opposite direction, from Nice to Monte Carlo, with a private tour guide. We started at St-Paul-de-Vence, scenic viewing of Cap-Ferrat, Eze, and ending with Voyager in Monte Carlo. You can do the same in reverse.
Although you would overshoot Nice to see St-Paul-de-Vence, I liked that town best. It's a little bit artsy-fartsy, but then so am I. You can even visit Marc Chagall there!
In Nice, we greatly enjoyed Oliviera, in Vieux Nice (Old Town) for dinner: https://oliviera.com/