This was definitely one of the best day trips! It's easy to catch the bus to Eze village where you hike down the Nietzsche Path to Eze-Sur-Mer and catch the bus or train back to Nice. Once in Eze village you can ponder around the 'chateau' (which is really a hotel) and ascend up to the very top of the mountain for spectacular views of the cote d'azur (see photo). Make sure you pay the small fee to get into the jardin exotique d'eze which hosts cacti and little plants before revealing the entire coast in beautiful sunlight. Once you've taken it all in, head down the Nietzsche Path; a rocky path for hikers only. Make sure you wear ankle supporting shoes. It'll take you just over an hour to reach the bottom with splendid views en route. Once at the bottom, cross over and visit the beach at Eze-Sur-Mer (Eze on the sea) before taking bus 100 or the train back to Nice. Overall it takes a good 3-4hours, best done with friends or family, but equally satisfying solo!