Villefranche, Cap-Ferrat, or Beaulieu-Sur-Mer?

All of those towns actually felt more touristy to me than Nice when I visited them this year in May because they are small. Most of the folks on tne street in Nice were locals. However, I can definitely understand your prefernce for basing in a smaller town.

Villefranche and Beaulieu both have train service as well as bus service, which would speed up your access to certain destinations along the Riviera (Menton, Antibes, etc.). Even for some of the hill towns, it can work better to start out by taking a train.

St.-Jean-Cap-Ferrat doesn't have rail service. I walked there from Beaulieu, so I don't know how good the bus service is, but I think you'll find it takes longer to get just about anywhere from St. Jean.

One thing to keep in mknd is that mid-October is way off-season for the Riviera. The weather may be very pleasant, but some transportation frequencies may be cut back, and some attractions will have significantly more limited hours. I noticed during my May visit that many museums, etc., were going to increase their hours of operation in June, and many were going to ratchet them up further for July and August.

I saw more of Villefranche than of the other two towns. There semed to be more old architecture, and I go to Europe partly for the Old World appearance. Cruise ships anchor offshore at Villefranche, though I don't know how much of that happens in October. Somehow, Beaulieu felt more built-for-tourists/expats. It's very clean and pretty, but I felt like everyone I saw on the street was probaby from the UK. Mind you, that was just an impression, based on nothing, really. And I assume Villefranche gets a lot more day-trip tourists, whereas Beaulieu seems the sort of place where people might stay for an extended time.

If you happen to be Nietzsche fans then you should stay in Eze and climb the chemin named after him that leads to the gate at the bottom of the village. Bus stops at the bottom of the path. He said that he thought up Thus Spake Zarathustra right there.

Villefranche will have the views but will also have day trippers and a fair number of tourists even in October. As you get out of the historic center, up into the hills, you'll get more typical apartments with less historic charm and perhaps not the out of the way feel you are looking for. Historic Eze will be the same, but with even more spectacular views (versus the section at the sea). October is a bridge season and you'll definitely notice less tourists overall.

On Cap Ferrat, you could focus around St. Jean, if you don't intend to venture out much (via bus). For a price, the views and lack of crowds.. The downside -- rainy days happen in Mid October and you'll have fewer options without a bus ride. I've only ever driven through the peninsula so I can't comment on bus service. You might also consider Menton.

We used Antibes as a base for the area and it was terrific. Some good restaurants, we found a cute apartment for less than we could in Villefranche-sur-Mer, and the trains took us where we needed to go: Nice, Monaco, Villefranche, etc. Lovely seafront.

I chose Juan les Pins. I found a small apartment that is 500 meters from the train station (for going up and down the coast), 2 min walk to the beach and walking distance to Antibes.