This paper proposes the data-driven tuning of low-cost Proportional-Integral (PI) fuzzy control of the payload position of tower crane systems using Iterative Feedback Tuning (IFT). A back-calculation and tracking anti-windup diagram is included to prohibit integrator windup and compensate for the process's dead-zone and saturation nonlinearity. A two-stage tuning strategy is proposed. In the first stage, the parameters of the fuzzy logic part of the PI fuzzy controller and the anti-windup tracking gain are optimally tuned in a model-based manner using an original version of the hybrid Particle Filter-Particle Swarm Optimization algorithm, improved by adding an information feedback model. In the second stage, the parameters of the linear part of the PI fuzzy controller are tuned in a data-driven manner using IFT, and then mapped to the remaining PI fuzzy controller parameters using the modal equivalence principle. The efficacy of the new data-driven fuzzy control strategy is demonstrated through experimental results, and the comparison shows the performance improvement over other strategies designed using competing optimization algorithms.