We went to Caladesi Island 3 years ago, its a gorgeous beach on an island and not much else, very relaxing, take a picnic. You have to go north of Clearwater through Dunedin to honeymoon Island where you pay to park, then catch a little boat over to the Island. I think in high season there is a boat from Clearwater but we went in February so had to use this one. We sat on the beach watching the dolphins playing.
If you want something with more than just the beach you may prefer Clearwater as there are bars restaurants, activities etc.