Need help with French Rivera plans

As noted, Cannes is in opposite direction of travel then Monaco and Eze.
We took a one euro bus ride to Monaco,,on the way back that same afternoon we stopped and had lunch at Eze Sur Mer.Eze has sort of two parts, the old town up on hill and the smaller strip along the water. You can either walk up to the old town or they have a bus. We chose to stay on beach so cant help with particulars. You can also choose to stop at several other places on the way to and from Monaco. Each time you board its one euro, which makes a bus trip with a few stops still cheaper then the train which is 4-5 euros for a one way. The train however does stop closer to the old town up on the hill of Eze. You don't have a ton of time to see everything,, really only two full days,, so I would choose to make some edits. One full day in Nice and one travelling either east or west( Cannes or Monaco) . you could do both, but you are then allowing only one afternoon in Nice.

Liz, I agree that you can go east easily by bus/train. I would probably explore Nice on Friday. On Saturday, bus to Eze Village and on to Monte Carlo. Then train or bus from Monte Carlo to Villefranch and on to Nice. As you have a specific time for leaving on Monday, I assume you are taking the train to Aix or Marseille. If so, I would rent a car and drive to Antibes, Cannes, Vence, and St. Paul-de-Vence and return to Nice. I would probably drive rather than train to Aix/Marseille. If you have already been to Cannes, I would take the A8 and then drop to the coast at St. Raphael/Frejus and drive through St. Tropez and Cassis.

Since you will be there on a Sunday, you must check what transport is available. We arrived by train to Antibes on Sun and there is no cab service. You must call a posted number, so have a phone that works and then wait. We waited over an hour. I would skip Cannes. My favorite spot was Vence, we had a car for that. Again check bus , train schedules for a Sunday and that may determine your itinerary. If you want to go to all those towns in 2 days you'll need a car. Monte Carlo is a must.

Do you have Rick Steves France or Rick Steves Provence and The French Riviera? If you don't have either one yet, get the latter book, as it has much more detail on the areas you mentioned in your post. Rick's books have extensive details about getting around this area. Be aware that there are "two Ezes" - the seaside town of Eze sur Mer and the hilltop village of Eze Village. It's the hilltop one you want to see. Monaco (Monte Carlo), Nice, and Cannes are connected by trains twice an hour. Monaco and Nice are connected by buses 4 times an hour; I think there are 2-3 buses per hour between Nice and Cannes, but the bus takes a lot longer on this run, so I'd use the train. Eze is the tricky one; there are something like 16 buses per day between Eze Village and Nice Monday through Saturday, and 8 on Sunday. Between Eze Village and Monaco, I think there are 8 buses Monday through Saturday and none on Sunday. Eze sur Mer is on the train and bus lines between Nice and Monaco, so that's easy, but then you have to get up to the village; there are something like 8 buses a day, or you can hike up (it looked quite steep to me, but others do it) or take a taxi.

Nice itself deserves more time than you are planning to give it. With that in mind, I suggest that you skip Cannes. Unless you want to stare at luxury beachfront apartments, private beaches, and yachts, Cannes has little to offer tourists. However, if you do want to go west, make a quick visit to Antibes. The walled old town is worth exploring on foot and, if you like Picasso, don't miss the Picasso Museum. Lignes d'Azur bus #112 runs between Nice and Monaco with a stop at Eze-le-Village, but it doesn't run on Sunday. On Saturday you could take a morning bus (07:00, 09:00, 11:00) from Nice to Eze-le-Village, visit the village, and continue on to Monaco, leaving the village at 09:30, 11:30, or 14:30. Explore Monte-Carlo and take either the train or bus #100 back to Nice. Or you could take bus #82 from Nice to Eze-le-Village. The earliest departure times are 06:30, 08:00, and 10:00. See the village and go on to Monaco on bus #112. (Bus #82 doesn't go as far as Monaco.) Again, remember that bus #112 doesn't run on Sunday.