MarGra, Easy to catch the train in Cannes. The station is only about four blocks back from the beach and is quite easy to find. The ride to Nice is about an hour each way and the train station in Nice is about 12 blocks (or so) back from the beach and Old Section. It is a little more difficult to find when returning from the Old Section, but folks will help you along the way.
Eze is going to be difficult. There is an Eze station and a shuttle bus that can take you up to Eze, but unfortunately the shuttle and the train schedule are not meshed well. You might be better off hiring a taxi in Nice and having the driver take you to Eze and then on to Monte Carlo where you can catch a return train to Cannes. This would be a full day and you would need to reconfirm schedules so that you make it back to the ship on time, but it would be memorable.
Hope that helps.