If you are planning on going fishing in South Tampa you really just need to get to the water. However, some places are more convenient than others.
Picnic Island Park offers opportunities to fish from a pier or you can wade out. Sunrise to Sunset.
Ballast Point has a nice pier, fish cleaning stations, and a small bait shop.
DeSoto Park will allow you access to McKay Bay fishing
Most of the area bridges will allow fishing, however some do not, just look for signage.