I have been trying to find information on the best way to get to Eze from Nice, bus or train?
Also would like to go right to the town and not the coast and take the hike because after we are planning to go to Monocco and then back on that coastal highway on the bus if possible.
You can take the train from Nice. It's not very far, there are many trains a day from Nice to Monacco, most all stop in Eze. It's inexpensive to take the take and one of the most beautiful train rides I ever experienced. Enjoy.
Several years ago I took the bus from Nice to Monaco. It was packed with sweaty people, stopped at every town along the way including EZE, and was a very interesting experience traveling as the local people do. The bus traveled closer to the coast than the train does. It took an hour to get to Monaco. I took the train back to Nice--it took a few minutes.