If you like a busy beach, then Clearwater or St. Pete Beach are a good bet. I prefer quieter beaches, so when I lived over there, I would go to the county parking areas at Sand Key, Indian Rocks Beach, Madeira Beach and Redington Beach. You usually have to pay to park at the county parks/lots, but you will usually find restroom and picnic facilities available there. For the best of both, spend a day on the quiet beach at Sand Key and then visit the restaurants and shops of Clearwater Beach which is just across a short bridge from Sand Key.
For a really relaxing beach day, Caladesi Island State Park is nice. It is off the coast of Dunedin (just north of Clearwater) and is only accessible by private boat or by ferry.