Questions about Côte d'Azur

Hi Lola,
Just answering your one of your questions, yes, there's a walking/hiking path up to Eze-le-Village. It's a significant elevation gain and is on a southern slope and so would be exposed to the sun, but it's May so perhaps it won't be terribly hot. Depending on the weather, you'd want to bring adequate water and probably have a hat that would shade the back of your neck as you are ascending.
The disadvantage of hiking is that there's a 5-star hideaway resort with two terrace bars (the beautiful people sleep here, it's that kind of place) with a jaw-dropping view of the coast below, but if you hike you'll arrive sweaty or worse, and they do have a dress code that they apply rigorously to non-guests.
An option would be to hike down, after you have a glass of wine at LaChevre d'Or.

Thanks, Kent! I assume you are talking about La Chevre d'Or? We would likely prefer to enjoy the view from outside anyway.

Where would we find the lower end of the footpath to start the hike up?

Lola,
Yes, I was referring to La Chevre d'Or. We were permitted to sit at a table and order wine from the one La Chevre terrace open to non-guests, and I'd have to say it was the best view with glass of wine I've ever had.
Look at the first post on this discussion thread, from a person who hiked down that trail, the trail I'm thinking of is called the Nietzsche trail:
https://community.ricksteves.com/travel-forum/to-the-west/nieztsche-trail-to-eze-do-we-dare

Lola,
We did not hike the Nietzsche trail. We were staying in Nice and took the train to the other Eze (the one on the coast) and then a bus up to Eze-le-Village.

It may be helpful to look at my 2007 post (the 2nd post) on the thread below
https://community.ricksteves.com/travel-forum/to-the-west/getting-to-eze
which has directions on how to get to Eze-le-Village by bus,
and also see Christy's post (same thread) on walking down the Nietzsche trail.

If you are into art I would also strongly recommend visiting the Maeght art museum in St Paul de Vence, and Magritte's chapel in Vence itself.

I much preferred the vibe in Juan-les-Pins to that of Antibes, but that's just me. Juan-les-Pins also has a sandy beach instead of a rocky one, if that helps you decide. There are frequent trains and buses between the two, so you can easily stay in one and spend lots of time in the other, or go back and forth whenever you wish.

I agree that if you want to make this trip about art, the Fondation Maeght should be on your short list.

My concern wouldn't be with the film festival - because I don't do movies, I suppose, but with the Monte Carlo Formula 1 circus which is usually about then, but I don't think next year's F1 calendar has be finalised yet.

If you are there during F1 week you should know that hotel rates shoot through the roof and the whole coast becomes a zoo.

If not, it could be fab, but warm.

Check which beaches have sand and which gravel or pebbles. Not nice (for me) on gravel or sharp pebbles.

My favourite walk is around Cap Ferrat.

Are you not interested in Renoir's final home?

Incredible views which match his paintings and a good look at his studio. Would be easy from Antibes.

Thanks everyone! I know the dates are not ideal, given events in the area. We would arrive May 26, a Thursday, after spending three days at the French Open. The Cannes Film festival ends on May 25 ( according to their website). It looks like the big Monaco car race would be that weekend; something we would definitely want to avoid!

So I know it is not ideal, but I don't know when else we would have a chance to visit this area----probably not before September 2017. If we don't go to Côte d' Azur after Paris, we could return to the UK and go walking in Wales. . . . or Cornwall . . . . or the Lake District. Those are all tempting too.

I'll see if I can find hotel prices for late next May. That may be the decider---we don't care to pay inflated event prices (unless we are going for the event).