Nice in October

Haven't been to Eze. Rick has a book that focuses just on southern France. I haven't read it, but he is usually super-good on logistics.

I believe your plan for the Cap Ferrat day is workable. I think I took the train to Beaulieu, walked to and visited both Villa Ephrussi de Rothschild and Villa Kerylos, walked at least part of the way around the peninsula, then walked to the Villefranche-sur-Mer RR station. I suppose I may have conflated two different day-trips (one to the villas, the other around the peninsula), but I still say your proposal is reasonable if you enjoy walking.

There are some little museums in the castle at Villefranche-sur-Mer. As I recall they were free in 2016. I thought Villefranche was visually more interesting than Beaulieu, but it would be good to see both.

Both bus lines 112 and 83 will get you to Eze le village from Nice. Be aware service on Sundays to Eze is sparse. Other days it runs about hourly. You can use the trip planner or download the app at lignesdazur.com for Nice’s bus lines.

You can get to the high village of Eze by bus, I have done it a couple of times. Just be sure to get the one going along the right corniche.

Typo in an answer above -- It's 82 / 112 to get to Eze le Village. Some people also take the train back by walking down the steep Nietzke trail. You can also take Uber there but getting one back I've heard is very difficult.

As of September 2nd, the Nice bus schedule and numbering scheme was completely scrambled to align around the new tram line. As a result, guidebooks and advice may be out of date. As mentioned, get the app -- it is geo-sensitive and updated. Noteably, line 81 to St. Jean Cap Ferrat is now 15. (Line 82 was unimpacted)

https://www.lignesdazur.com/en/new-network-the-new-lines-numbers/1041

Your day to Villefrance-sur-mer and Cap Ferrat should work out well, in terms of timing.

I took the train to Villefranche and back. I think the train also stops in Beaulieu.

I just did the bus to Villa Ephrussi Rothschild, etc. a few days ago. Yes, the bus number is now Bus #15, and you catch it in Nice behind a Monoprix off of the Garibaldi tram stop. (Confusing - a nice French woman helped me with directions.). That bus will leave you very close to the Villa. Again, ask someone on the bus when it starts looping around town for the correct stop. Fantastic gardens at the Villa and such a beautiful setting! I got there when it opened and was able to take several photos before anything was crowded.

I wanted to take the bus afterwards to Monaco, but I couldn’t find the bus stop, so I did the walk further east. I finally found a bus stop just heading back to Nice, so I combined my Menton day with a stop at Monaco on the way back. (Train to Menton, bus to Monaco, bus to Nice.). Menton was one of my favorite towns to visit - relaxing and a gorgeous Italian section to explore!

I should add that Menton has their own microclimate, so if the forecast looks bleak, you might want to head there for the day.

Menton has a couple of very nice gardens. Both are on hillsides, though, and not really recommended for folks with significant mobility challenges. I enjoyed Menton a lot, but the historic center is extremely touristy.

Thank you to everyone for their input; very helpful information!