I have not explored the rivers in the region very well. I do know the Myakka River is a good paddling locale. It is about an hour south of Tampa. Water levels have been good this winter.
A friend of mine has paddled a few rivers in that area:
Hillsborough River near Tampa..put in at Sargeant Memorial park take out at Trout Creek,
Weeki Wahee River,
Withlacoochee River (south),
Weedon Island Canoe Trail,
Manatee River,
Chassahowitzka River,
Homosassa River,
Crystal River,
Braden River,
Halls River