We present molecular-simulation-based calculations of the Van Hove correlation function (VHF) of water using multiple modeling approaches: classical molecular dynamics with simple three-site nonpolarizable models, with a polarizable model, and with a reactive force field; density functional tight-binding molecular dynamics; and ab initio molecular dynamics. Due to the many orders of magnitude difference in the computational cost of these approaches, we investigate how small and short the simulations can be while still yielding sufficiently accurate and interpretable results for the VHF. We investigate the accuracy of the different models by comparing them to recently published inelastic X-ray scattering measurements of the VHF. We find that all of the models exhibit qualitative agreement with the experiments, and in some models and for some properties, the agreement is quantitative. This work lays the foundation for future simulation approaches to calculating the VHF for aqueous solutions in bulk and under nanoconfinement.