Indian Rocks and Madeira Beaches are very nice and right on the Gulf, so the water gets quite warm. There are condos and houses for vacation rentals as well as hotels. It is a bit outside the city of Tampa so you may want to rent a car there. But there are a lot of restaurants and it's not so far that you can't head into the city to see the sights.
While visiting Tampa you simply can't miss the beach. Maybe go a little south of the city and try the beaches of Sarasota or Bradenton. The water here at the Gulf Coast is warmer than at the Atlantic coast of Florida.
What good is a trip to Florida of you do not experience the sea? My favorite place for this is Clearwater. It has long stretches of white sandy beaches which are replenished manually each each. Why replenish you ask? It is because some hotels along the shore line decided to setup barriers to form their own beaches interfering with the natural cycle of erosion and replenishment. Just a little bit of geology lesson for you :)
Beaches just a minutes away. The Florida Aquarium, Channelside, and historic Ybor City, a cigar museum, a museum of science and natural history, the county historical museum, and two racetracks.
Cruises, waterfront cafes,nightnightlife, fishing, boating, golf.