We were in Nice just last week. Our ship docked in Monte Carlo. I agree with Hank that the best way to see Nice is on foot. (Actually, that would be true for many of your other ports, as well.) We made a wonderful stroll down the promenade by the water, which is simply beautiful, and then walked around the old town, playing it by ear. For instance, we found a small restaurant along one of the narrow streets where we enjoyed a fabulous Quiche Lorraine. Just be aware that some of the streets are steep, although many we encountered had steps that made it easier, so wear comfortable, sturdy shoes. Also, as Hank mentioned, it's easy to get lost in old town, so remember the landmarks you pass along your route.
By the way, from your earlier post, it appears you are not docking in Nice, but in nearby Villefranche.
Villefrance,France- What to do here?
Be sure to leave plenty of time for your return trip.