Rent bikes at one of the two bike shops in Palm Beach and take the bike trail which circles the island. Lovely views of the inland waterway, Palm Beach marina and extraordinary close up views of peoples boats and homes. Visit Palm Beach Gardens Mall for excellent shopping.Visit the Flager museum. Have dinner at Charleys Crab.Oogle the purple rinse brigade on Worth avenue and remember to stick to the speed limit 20mph. There are speed traps everywhere on the island.