At. Jean Cap Ferrat

I am not sure where you are staying, but check if you are within walking distance (or if your hotel provides a transfer) to one of the train stops Beaulieu-Sur-Mer (more likely), or Villefranche-Sur-Mer. That would open up easy travel to Nice, Monaco, Menton, Antibes, Cannes, etc., as well as Italian areas near the border.

We were in Nice for 2 weeks just prior to the February Carnival (low season), and we had to wait for multiple buses (bus #15) to St. Jean Cap Ferrat due to the number of people waiting. I don't think this is the experience you want to have with luggage and a potentially reluctant spouse. The train may be better, but it also might be a good idea to look into a transfer/taxi/Uber.

Another note is that the train can get very busy with commuters during rush hours, particularly on travel to/from Monaco.

I spent just a few hours in Jean Cap Ferrat on a day trip from Nice last October. The weather was wonderful, warm and sunny. I thought it would be a lovely place to stay for a few days. The tourist information office was very helpful and friendly. They might be able to help you with the activities and tours you are asking about. Day trips by bus, or bus and train should be quite easy to Nice, Monaco, Eze and others. There is a train station in nearby Beaulieu-sur-Mer which is a 30 minute walk on a lovely coastal path or a short bus or taxi ride. You can get a Pas Zud explore pass that will cover all regional train and bus travel between and within towns. I think is is about 50 Euros for 7 days.

I appreciate both responses a lot. I am planning on getting an Uber from airport to Brisne Marine Hotel and then finding information center.

Somehow "affordable" and Saint-Jean-Cap-Ferrat don't seem to me to belong in the same discussion. I'm certain the hotel and the time you spend in the immediate environs will be nothing short of magical, but don't expect the process of getting from there to anywhere else you want to visit to be either inexpensive or convenient.

I have never been to France and foolishly got locked into hotel before I did enough homework which is related to my concerns and request for advice.

If you are interested in architecture and history, do not miss Villa Ephrussi and Villa Kerylos, both essentially walking distance for you. There is a public bus service making various stops at St. Jean, which can be quite hilly at the center, and from Beaulieu, you can take the #100 bus all the way to Nice, or, in the other direction to Monaco (skippable IMHO) and Menton (totally worth a day trip). OR the train, which is faster and still quite cheap. Antibes' Picasso Museum would be a day trip, as would also be Eze Village, with its fabulous views and perfume factory tour. If you are spending for taxis and/or Ubers, consider splurging for a day trip to St. Paul de Vance, with its amazing Fondation Maeght. That is, only if you have already done the Matisse and Chagall museums at Nice.
It will still probably be warm enough to swim, by the way. And as someone else noted, the cape features some of the most luxurious private homes on the Riviera, meaning restaurants and shops will be priced accordingly.
Since you are staying on penninsula more or less isolated from the mainland, there will not be a walkable tourist information booth. Have coins and/or small bills to pay aboard Bus #15, which will take you all over the place, and allow you to transfer at train station. https://transitapp.com/en/region/nice/lignes-d-azur/bus-15
It's not as horrible as it sounds: you are staying in the French equivalent of Beverly Hills.

I am so grateful for the specific helpful information. Merci