There are several options. The Zachary Taylor Nation Park is on the Navy Reservation beyond the Truman compound are where some ships berth. Shaded, picnic tables refreshments, shieled by a breakwater and a jetty, snorkling available. We rrent bikes on Duval St and ride there.
In addition, you can to go the beaches on the south end. See the map at
<http://www.fla-keys.com/maps/images/KeyWestOldLg.jpg>
Higgs beach is in a park area with shelters available.
We spent a week there several years ago and rode bikes everywhere.
Some of the hotels will let you use their beaches, too. Hyatt Pier House, which has tops optional, and Wyndham Casa Marina, near the southernmost point, formerly the Marriott <http://www.casamarinakeywest.com/intro.html>