Caladesi Island State Park is not a place tourists visit often--but they should. It's accessible only by boat, which cuts down on crowds considerably. You can take a boat from Honeymoon Island State Park; it's $8 per adult (round trip) or $4.50 for children. Caladesi Island is one of the only remaining completely natural beaches in Florida, and the beauty is sublime. You can hang out on the beach, you can enjoy 3 miles of hiking trails, and you can even enjoy a snack at the concession area. Caladesi is quiet, peaceful, natural, beautiful, and refreshing.
The boat ride is a lot of fun also. It's only about 10 minutes, but kids love it (and adults do, too). We saw dolphins on both the trip over and the trip back. Our favorite park was hiking the nature trails--we only saw one other couple out there. But hanging out on the beach was a close second! My only advice--don't wait for the last boat to take you back home, because it will be PACKED and you may have to wait a while. Try to get the one that leaves 30 minutes before the last boat.