Tom,
From what we were told, the biking from Antibes to Nice was not so great, hence we went west to Cannes. I would concentrate on going east from Nice or taking the train west and then getting the bikes.

We went out on the water from Antibes (basically rented a dinghy) and went around Cap d Antibes. Billionaires Bay was lovely.

If you get a bigger boat you can get to the Lerins Islands. Most day trips, we found either left from Nice or Cannes. Alot of them came to Antibes, but since we were staying there it didn't help us much. The harbor in Antibes is amazing if you like to look at yachts. Have some pictures of the 90m Dreamboat. Nothing like a row of 200+ foot yachts lined up.

Have a great time, such fun and the food and drink. Baguettes and cheese 3 times a day!
Ellen