Nice and near by towns itinerary for 5 days

Hi,

We are visiting Nice for 5 days during the first week of May.

Request for feedback on the below itinerary.

1. Nice
2. Antibes and Grasse
3. Eze and/or Menton
4. Gordes du Verdon - it will be a long day, but we wanted to visit the place once
5. Nice

Are Antibes and Grasse doable in one day? And Eze and Mention also in a day possible?
We plan to rent car just for day 4 while going to Gordes. Rest of the days we use public transport.

Regards,
Kavya