If you own a kayak I would recommend the Hillsborough River. I would divide the river into three sections; below the spillway, above the spillway and in the State Park. Each of the sections is markedly different from the other and all of them are worth the trip. You can throw your yak in the water at any of the parks along the river. Remember, paddle upstream first.
If you do not own a kayak and would like to rent one, there are several places you can do this. Canoe escape is a very popular location and they offer a variety of trips. The Hillsborough River Park also offers canoe rentals.