Key Biscayne, Miami
I found Bill Baggs Cape Florida State Recreation Park on Key Biscayne provided a quiet respite from the bustle and pretentious atmostphere of South Beach. Unlike South Beach, Key Biscayne was calm, peaceful and relatively secluded. There is a bike path that runs along the beach and a facility where you can rent bikes as well as beach chairs and umbrellas.
This island has the Seaquarium, park, exclusive residential developments, as well as incomparable views of the city.