Tenoroc is a county-owned facility that stopped throwing registered a few years ago. Scenery-wise it is very nice; most stations are in the shade of big live oaks. They also changed managers about a year or so ago, so it would be wise to call and see what they are still doing.
Tampa Bay Sporting Clays is a little further, but besides three levels of targets, they also have a regulation bunker trap, and a FITASC parcour.
Tampa does have rental guns available.