Check out ExecuCar or SuperShuttle to get to downtown St. Pete from Tampa International Airport (TPA) or St. Pete-Clearwater International Airport (Pie). A rental car isn’t really necessary if you’re sticking to the burg. However, there is plenty of cheap parking if needed.
Getting around St. Petersburg is pretty easy considering that most of the action is packed within an area less than two square miles. To get around, I would pick Uber or Lyft over a taxi even though all you really need is your two feet and the Central Ave Trolley (CAT) which runs east west through the center of St. Pete.