Anclote Key is a great spot to spend your day. Anclote has an abundance of white sandy beaches for you to enjoy your day.
The Anclote sandbar is just north of Anclote Island. This is another amazing place to spend your day on the water. Can get pretty packed during the weekends, but the weekdays you might have the sandbar to yourself.
North tip of honeymoon is now only accessible by boat so the crowds during the week are small. Caladesi Island has amazing beaches on the north tip as well that are only accessible by boat or the ferry.